jack said:
Are these correct? If not, why?
1. Thank God. (Why is this correct?)
2. Thank Jack. (How come this is wrong?)
3. Thanks God.
4. Thanks Jack.
1. and 2. are OK (i.e., Ask God/Jack for thanks. Thank them/him (Verb + Object)):
Thank God.

(Do this: Give thanks to God)
Thanks
, God.

(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.
Thanks
, God/Jack.
Note that, "Thanks" is a noun:
I am giving/sending my
thanks to God/Jack.
Thanks Jack (
My thanks to Jack)
Thanks, Jack. (
Thank you form Jack)
All the best,
