In Romans 1:18, Paul starts his dissertation by going back to the revelation of God at the beginning of creation.

¹⁸ For the wrath of God is revealed from heaven against all ungodliness and all unrighteousness [injustice] of men, who suppress the truth in unrighteousness, ¹⁹ because that which is known about God is evident within them; for God made it evident to them.

The truth of God is actually in all men, and it is known by instinct. The original revelation of God given to Adam has a residual effect upon all, though time and idolatry has encrusted it, making it often difficult to re-discover. Yet anyone who truly seeks the Creator must contemplate the idea of good and what is equitable justice for all. Man is a reasonable creature, and when his reasoning faculty is functioning properly, he is able to look at creation and see a Creator. He sees beauty and knows that God is both wise and good. He sees human relationships, happiness and oppression, and is then able to understand the meaning of treating people equitably and justly.

God's Laws are Self-Evident

In other words, the laws of God are self-evident, even to those who are "without law," that is, without having direct knowledge of the divine law as revealed to Moses. Paul makes it clear that God has revealed Himself to all men on some level, and God thus holds all men accountable according to their level of revelation.

²⁰ For since the creation of the world, His invisible attributes, His eternal [aidios, "perpetual"] power and divine nature [theiotes, "Deity"], have been clearly seen, being understood through what has been made, so that they are without excuse.

Creation is God's way of making His presence and power known to all men in a self-evident way, so that even illiterate people can understand Him on some level. He is "understood through what has been made." Unfortunately, because men reject Him, they tend to outsmart themselves by the idea that they will only believe what they can analyze and understand. Such "scientific" thinking presumes that the mind of man is equal to or greater than the mind of God, and it presumes ahead of time that man is, in fact, a god in himself.

When people do not believe in God, they make gods out of men, created in their own image, and Paul says, "they are without excuse."

Defining Some Terms

The Greek term, theiotes, translated "divine nature" in verse 20, has a numeric value of 592. When one adds to this the numeric value of Iesous (Jesus), which is 888, one comes to 1480, the numeric value of "Christ." In other words:

Divine Nature + Jesus = Christ

592 + 888 = 1480

When we link the Divine Nature to Jesus, we see that He is the Christ, who is the earthly expression of God Himself.

Take note also that the divine power is said to be aidios, rather than aionian. Paul says that His power is perpetual, as Young's Concordance defines the term. This is one of the closest words to the idea of infinite time that the Greeks had at their disposal. Paul avoided the term aionian in this case, because it usually (if not always) has to do with a specific age. Young consistently renders the term "age-lasting" in his translation. But in Romans 1:20, he renders aidios "eternal."

Paul thus makes it clear that God's power is aidios, "perpetual," or unending. The root of the word is aei, which means "without fail." Hence, Stephen said in Acts 7:51, you are "always resisting the Holy Spirit." Always (aei) is not infinite time per se but "without fail."

The Roots of Perversion

Paul does not attempt to prove the existence of God, but adopts the same argument that is seen in Genesis 1:1. Creation itself proves the Creator, and anyone who doubts this is not being reasonable. But more than this, he shows how men perverted their perceptions of God and His righteous character.

²² Professing themselves to be wise, they became fools, ²³ and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures.

There were bird-headed gods in Egypt. The Egyptians also worshipped four-footed animals, such as Apis, the bull. They also worshipped the scarab beetle. The Wikipedia reads,

"It seemed to the ancient Egyptians that the young scarab beetles emerged spontaneously from the burrow where they were born. Therefore they were worshipped as "Khepera", which means "he was came forth." This creative aspect of the scarab was associated with the creator god Atum."

http://www.egyptianmyths.net/scarab.htm

The basic principle of Law, expressing the mind and will of God, is that the judgment must always fit the crime (sin). When men worship man, bulls, and beetles, they attribute these earthly attributes to God (actually, their "gods"). Therefore, the Creator does the same thing to such men. If they want to worship flawed gods, then God will show them their flaws by giving them the desires of their hearts. By so dishonoring God, God turns the tables upon them, "that their bodies might be dishonored among them." Men worshiping men.

The Problem of Homosexuality

²⁶ For this reason God gave them over to degrading passions; for their women exchanged the natural function for that which is unnatural, ²⁷ and in the same way also the men abandoned the natural function of the woman and burned in their desire toward one another, men with men committing indecent acts and receiving in their own persons the due penalty of their error.

In other words, homosexuality, Paul says, is the physical result of man's belief that he is his own god and the measure of the universe. While this "unnatural function" has been in the world for a long time, its prominence in various civilizations is in direct proportion to the idea that man is his own god.

One only needs to look at the Roman emperors for many examples. The emperors were worshiped as gods, and a great many of them, including Nero himself, were homosexuals, according to the Roman historian Suetonius, who wrote of Nero,

"He castrated the boy Sporus and actually tried to make a woman of him; and he married him with all the usual ceremonies, including a dowry and a bridal veil, took him to his home attended by a great throng, and treated him as his wife. And the witty jest that someone made is still current, that it would have been well for the world if Nero's father Domitius had had that kind of wife. This Sporus, decked out with the finery of the empresses and riding in a litter, he took with him to the courts and marts of Greece, and later at Rome through the Street of the Images, fondly kissing him from time to time."

Perhaps Paul had Nero in mind as he wrote these verses, but it would have been treasonous for him to say so. Though Paul did not quote from the divine Law itself, we know that he was well schooled in the Law and understood the mind of God on this question. Lev. 18:22 says,

²² You shall not lie with a male as one lies with a female; it is an abomination.

Lev. 20:13 provides us with a double witness,

¹³ If there is a man who lies with a male as those who lie with a woman, both of them have committed a detestable act; they shall surely be put to death. Their bloodguiltiness is upon them.

Many today attempt to justify homosexual acts as "normal," with the goal of making it a crime to call it a sin. While I do not advocate violence or meanness toward anyone, including homosexuals, neither can I compromise the Scriptures by putting away the Law. I should also add that Christians are not to attempt to enforce the divine Law prior to its establishment as the law of the land. We live in a Babylonian society and are duty-bound only to learn and remember the divine Law for a future time.

Meanwhile, of course, rather than merely criticize homosexuals, we ought to pray for their healing. Individual homosexuals today are paying the price for the sins of their fathers. Many of them want to be healed of this affliction, even though others are insulted by the very suggestion that they need healing. For our part, it is important to view all sinners as God views them, and to view all sin as God views it. True Christians do not have the right to establish laws or moral views that are inconsistent with the mind of God as expressed in His Law.

We must also keep in mind the distinction between being homosexual and practicing that life style. The Law of God does not judge anyone for being homosexual, but only for its practice.  The solution (while they await healing) is to abstain from sinful acts and relationships, even as many people in the past have remained unmarried for various reasons.

²⁸ And just as they did not see fit to acknowledge God any longer, God gave them over to a depraved mind, to do those things which are not proper, ²⁹ being filled with all unrighteousness, wickedness, greed, evil; full of envy, murder, strife, deceit, malice; they are gossips, ³⁰ slanderers, haters of God, insolent, arrogant, boastful, inventors of evil, disobedient to parents, ³¹ without understanding, untrustworthy, unloving, unmerciful.

So homosexual behavior is just one of many sins of the "depraved mind" of man. All of these sins are forbidden by biblical law, as Paul says in the next verse,

³² and although they know the ordinance [dikaioma] of God, that those who practice such things are worthy of death, they not only do the same, but also give hearty approval to those who practice them.

The Greek word, dikaioma, means "that which has been deemed right so as to have force of law" (Thayer's Lexicon). Those who practice homosexual behavior know that it is wrong, even if they try very hard to justify their actions. Hence, they are accountable to God for their actions, Paul says in the next verse: "Therefore, you are without excuse."

Even those who despise the divine Law know that one ought to keep the Law. Few would justify first-degree murder, for instance, even if their doctrinal position says that the Law has been put away. For most Christians, the real motive in putting away the Law is to retain the right to discard any particular law that they find disagreeable.

When the Church reserved for itself the right to judge the Law and mind of God, and to decide by their own "conscience" which of the laws they wanted to keep and which to discard, they lost the moral right to condemn any sin. It is hypocritical to cast aside the Law of God and then judge other sinners by that same Law. The church thus laid the foundations of lawlessness (anomia) which are now in full bloom in the world today.