One argument that is presented is Jesus cannot be God because he died.
Firstly, this is a deceptive question because a Unitarian (usually a "Christian" or a Muslim) who is not influenced by soul sleep will acknowledge that a person dies goes to Sheol where the person is still fully conscious. I assume one of the Unitarians I spoke to believes hell and Sheol are the same thing but that's another topic, I would need to know his position on that a bit better.
Anyway, Death in a Christian context doesn't mean ceasing to exist, death is biological cessation. It is not heresy to say God died provided death is correctly defined. Jesus as the God-Man did NOT cease to exist. A Unitarian "Christian" I once spoke to on Paltalk if I recall admited that Jesus went to Sheol. If he is in Sheol, Jesus would still be fully conscious and communicate with others who were there. It is only heresy to say that God ceased to exist, not to say he died.
God is not a man!!!
The next objection I want to tackle is Numbers 23:19 which is often MISUSED to attack Jesus being God. First of All, God taking on human flesh doesn't negate his divinity. Jesus was still God but his deity did not vanish when he took on flesh. Furthermore Trinitarians don't worship flesh, we worship the Holy One who tabernacled among us (John 1:14) We agree God is not a man, but this doesn't mean he cannot take on a human nature and still be God. Secondly the context is saying that God isn't like man, he never lies like man does. If God says he is going to do something, he will deliver, this can also be found in Hosea 11 and 1 Samuel 15. A question to the Unitarians, can God become man and still remain fully God and not cease being God? If not, why not? If you are going to say it makes no sense, well God existing from eternity makes no sense either, and you have to reject it on that basis.
How can Jesus be God if he has a God?
Another point of contention is Jesus is a distinct person from the Father, which is what Trinitarians believe.
At least Unitarians can agree that the Modalists are in error on this point. Where the Unitarians are going into unbiblical doctrine however, is using this to deny Jesus as God. When Jesus took on flesh according to Philippians 2, he emptied himself of his divine prerogatives and took the form of a slave, reclaiming them after going back to heaven and to this day relates to the Father as his God because in Revelation he is still the God-Man.
He is both the Alpha and the Omega but also subservient to the Father in terms of position and rank, not essence and nature. Jesus relates to the Father as his God by virtue of the fact he is fully human and he identifies himself as the Alpha and Omega much like YHWH, Identifies himself with the Ego Eimi sayings of Isaiah 41:4, Isaiah 43:10, Deuteronomy 32:39 and others by virtue of being God. Although translations differ, that's another issue altogether.
James White in his book the Forgotten Trinity and a talk that Sam Shamoun has done on my YouTube account, they go into greater deal than I do. I also will post James White's video on "The Carmen Christi and Harpagmos" which goes into detail regarding the subject of Philippians 2 in case you want to dispute what the text is talking about:
The Carmen Christi and Harpagmos:
Sam Shamoun on John 8:58 and Exodus 3:14 section 1
Sam Shamoun on John 8:58 and Exodus 3:14 section 2
What about Moses, Satan and others called Gods?
In the context of angels and men, they are ordinary lords, the same thing with the "Moses made a god" statement. This doesn't mean Moses is God like YHWH, it refers to him being a representative of YHWH. Satan is referred to as the god of this world in 2 Corinthians 4:4 in the NT but this doesn't make him in nature god, so using this as a refutation of John 1:1 is a red herring. Any reference to someone being called god or lord is defined by it's context. It is evident from the NT that Jesus is NEVER referred to God in this way, but is actually identified as God as the Father is, but is distinguished from the Father in person-hood. The only exception would be Psalm 45 which I have written on here: http://answering-judaism.blogspot.co.uk/2013/11/triad-of-texts-nature-of-jesus.html
The Trinity was invented at the Council of Nicea
The next point I would like to address is the common assertion that the Council of Nicea is where the Trinity was conjured up, which is another bald faced lie presented by the Unitarians. Nicea did not invent the Trinity, it was convened to deal with the subject of Arianism as one of the many topics. InspiringPhilosophy has done a video on this topic and demonstrates this fact: http://www.youtube.com/watch?v=WSKBGdv07nQ
Feel free to look at this video and judge for yourself.
Nicea itself dealt with Arius' heresy quite effectively but this didn't stop the Arians from trying to wipe out the Trinitarians because of the Arians being given pre-eminence over the Trinitarians BY CONSTANTINE, which most Unitarians conveniently fail to mention. The Arians, though fewer in number, had greater power with Constantine even being baptised by Eusebius of Nicomedia, an Arian, not to be confused with Eusebius of Caserea, who himself was present at Nicea. InspiringPhilosophy speaks more about this issue in depth in the video above.
More articles on the Trinity will be posted here in the future Lord Willing.
Hope this has been a help to you.