1. and 2. are OK (i.e., Ask God/Jack for thanks. Thank them/him (Verb + Object)):Originally Posted by jack
Thank God. :D (Do this: Give thanks to God)
Thanks, God. :D (Thank you from God)
Thank Jack is OK (i.e., Do this: Give thanks to Jack for all his help). Mind you, Thank God! or Thank God is an idiomatic expression.
If 3. and 4. mean, Thanks from God/Jack, as in the closing of a letter or an email, then a comma is required in order to separate the object of 'from' from the noun "Thanks".
Thanks from God/Jack.
Note that, "Thanks" is a noun:
I am giving/sending my thanks to God/Jack. :D
Thanks Jack (My thanks to Jack)
Thanks, Jack. (Thank you form Jack)
All the best, :D