Thou shalt make no covenant with them, nor with their gods.
It is essential that we understand what a covenant was and what a god was in order to understand the meaning of this verse. The word covenant in the Old Testament is from the Hebrew word ber-eeth which is translated covenant 264 times. But it is also translated league 17 times and even confederacy once. League is used in the sense of a treaty and in fact that is what a covenant means.
It is from the Hebrew word barah which means "to eat, consume". When you contract rights and responsibilities given to you by God to another you become less of a person. The person who has taken on your responsibility also has your corresponding right. The right still exists but the manner in which it is exercised now involves a second party.
In the New Testament the word translated into covenant is diatheke and is also translated testament. It is defined "a disposition, arrangement, of any sort, which one wishes to be valid". A second definition is "a compact, a covenant, a testament".
The second question is what is a god. The terms God and gods are come from the same Hebrew and Greek words. The translators arbitrarily determine if the word should be made singular or plural, be capitalized or small case.
In the case of both elohim, in the Hebrew, and theos, in the Greek, both words were used every day in reference to magistrates and judges in courts of law. These human judges were the "gods many" spoken of by Paul. They were simply men who ruled over the lives of other men through institutions men made for themselves. They did this by making laws, forcing contributions, and subjecting men to the will of men.
The command to make no covenants with them or with their gods is brought into a modern context through the series entitled Covenants, Contracts, and Constitutions.
Two Souls, Two Systems
Deceptions and Delusions
Roasting the Sacred Cow