I’ll never see them again probably will work better. I think the grammar allows for either one but them again sounds more natural. “Those” and “These” are going to be used when you repeat the noun: those eyes, these eyes. “Them eyes” is no good. Otherwise I can’t think of a good rule for you.

I'll never see them again

I understood what you ment after reading last sentence, so "I will never see them again" is correct. Those and these is used with nouns. For example: I will never see these eyes again.