Paul says there are Gods many and Lords many. I want to set it forth in a plain and simple manner; but to us there is but one God—that is pertaining to us; and he is in all and through all. But if Joseph Smith says there are Gods many and Lords many, they cry, "Away with him! Crucify him! Crucify him!" Mankind verily say that the Scriptures are with them. Search the Scriptures, for they testify of things that these apostates would gravely pronounce blasphemy. Paul, if Joseph Smith is a blasphemer, you are.
I say there are Gods many and Lords many, but to us only one, and we are to be in subjection to that one, and no man can limit the bounds or the eternal existence of eternal time. Hath he beheld the eternal world, and is he authorized to say that there is only one God? He makes himself a fool if he thinks or says so, and there is an end of his career or progress in knowledge. He cannot obtain all knowledge, for he has sealed up the gate to it. Some say I do not interpret the Scripture the same as they do. They say it means the heathen's gods. Paul says there are Gods many and Lords many; and that makes a plurality of Gods, in spite of the whims of all men. Without a revelation, I am not going to give them the knowledge of the God of heaven. You know and I testify that Paul had no allusion to the heathen gods. I have it from God, and get over it if you can. I have a witness of the Holy Ghost, and a testimony that Paul had no allusion to the heathen gods in the text" (Joseph Smith, The Teachings of the Prophet Joseph Smith. p. 370-371).
As you can see, he believed the passage referred to real gods that exist. This, however, does not negate the fact that we only have one God the Father and one Lord Jesus Christ. He also made clear that he knew his critics believed that the passage had reference to heathen or false gods. He denies that saying he received by revelation the fact that it didn't have reference to them.
The criticism he mentioned is still the same today. I quote from CARM:
The key to understanding this scripture is the term "so-called." Paul is teaching us that there are not many gods. Rather, he is teaching us that there are many that are "called" gods but are not really gods. We can see this elsewhere when Paul says in Gal. 4:8, "Formerly, when you did not know God, you were slaves to those who by nature are not gods." We can see that the Bible teaches that there is only one God, yet people believe in other gods. In reality these other gods do not exist.
What is so interesting about this debate for me is the fact that the renowned scholar, disciple, and Christian Origen (185-251 AD) also believed the passage had reference to real gods.
There are some gods of whom God is god, as we hear in prophecy, "Thank ye the God of gods," and "The God of gods hath spoken, and called the earth." Now God, according to the Gospel, "is not the God of the dead but of the living." Those gods, then, are living of whom God is god. The Apostle, too, writing to the Corinthians, says, "As there are gods many and lords many," and so we have spoken of these gods as really existing. Now there are, besides the gods of whom God is god, certain others, who are called thrones, and other called dominions, lordships, also, and powers in addition to these.(In Ante-Nicene Fathers [ANF] 9:315)
This divinity of mankind is made possible through Jesus Christ (the "first-born of all creation"). He was the first to become divine.
And thus the first-born of all creation, who is the first to be with God, and to attract to Himself divinity, is a being of more exalted rank than the other gods beside Him, of whom God is the God, as it is written, "The God of gods, the Lord, hath spoken and called the earth." It was by the offices of the first-born that they became gods, for He drew from God in generous measure that they should be made gods, and He communicated it to them according to His own bounty. The true God, then, is "The God," and those who are formed after Him are gods, images, as it were, of Him the prototype. (ANF 9:323)
Apparently some landed the criticism that this doctrine would somehow demote God and make him less than what He is (much the same way the LDS have been ridiculed for "demoting" God). Origin responded:
Now it is possible that some may dislike what we have said representing the Father as the one true God, but admitting other beings besides the true God, who have become gods by having a share of God. They may fear that the glory of Him who surpasses all creation may be lowered to the level of those other beings called gods. (ANF 9:323)
I find it interesting that this concept of "thrones," "dominions," "powers," etc also appear in LDS scriptures, but not in the Bible, especially in the context of the plurality of gods and/or exaltation.
A time to come in the which nothing shall be withheld, whether there be one God or many gods, they shall be manifest. All thrones and dominions, principalities and powers, shall be revealed and set forth upon all who have endured valiantly for the gospel of Jesus Christ. (D&C 121:28-29)
And again, verily I say unto you, if a man marry a wife by my word, which is my law, and by the new and everlasting covenant, and it is sealed unto them by the Holy Spirit of promise, by him who is anointed, unto whom I have appointed this power and the keys of this priesthood; and it shall be said unto them—Ye shall come forth in the first resurrection; and if it be after the first resurrection, in the next resurrection; and shall inherit thrones, kingdoms, principalities, and powers, dominions, all heights and depths—then shall it be written in the Lamb’s Book of Life, that he shall commit no murder whereby to shed innocent blood, and if ye abide in my covenant, and commit no murder whereby to shed innocent blood, it shall be done unto them in all things whatsoever my servant hath put upon them, in time, and through all eternity; and shall be of full force when they are out of the world; and they shall pass by the angels, and the gods, which are set there, to their exaltation and glory in all things, as hath been sealed upon their heads, which glory shall be a fulness and a continuation of the seeds forever and ever.
Then shall they be gods, because they have no end; therefore shall they be from everlasting to everlasting, because they continue; then shall they be above all, because all things are subject unto them. Then shall they be gods, because they have call power, and the angels are subject unto them. (D&C 132:19-20)
A search of the Bible does not turn up such terminology: http://scriptures.lds.org/en/search?type=words&last=%22thrones%22%2C+%22gods%22&help=&wo=checked&search=thrones%2C+dominions&do=Search&iw=scriptures&tx=checked&af=checked&hw=checked&sw=checked&bw=1 except in Col. 1:16 which does not mention gods or exaltation.
Irenaeus also had something to say about the issue of exaltation and uses terminology also found in D&C 132.
For there is the one Son, who accomplished His Father's will; and one human race also in which the mysteries of God are wrought, "which the angels desire to look into;" and they are not able to search out the wisdom of God, by means of which His handiwork, confirmed and incorporated with His Son, is brought to perfection; that His offspring, the First-begotten Word, should descend to the creature (facturam), that is, to what had been moulded (plasma), and that it should be contained by Him; and, on the other hand, the creature should contain the Word, and ascend to Him, passing beyond the angels,and be made after the image and likeness of God. (ANF 1:567)
It would seem that this is a repeat of the doctrine that the Word became man so that men may become gods (or "Words"). Interestingly, we must "pass beyond the angels" in the process. This is similar to the terminology in D&C 132:19-20.