No, double modals are never acceptable in standard English. There are some dialects that use them.
Note that modals are followed by the bare infinitive, but modal verbs don't have infinitives of any kind (at least, in standard English).
One of your examples is not a true double modal:
Could I thought you might help me?
The two modals are in two separate clauses. We can say "Could I have thought (that) you might help me?" or (less likely) "Could I think (that) you might help me?". These are fine once "thought" is replaced with the bare infinitive "think" (as in "I could think").
As for your other examples, none are acceptable in the standard language.
I thought you might could help me.
We would replace "could" with the infinitival phrase "be able to". The same is true of all the other "might could"s.
Could I might do that?
This one is an inverted example of "could might" (rather than "might could"). I suppose it would mean something like "Could it be possible for me to do that?".
You might should eat before you go.
We should say "You might have to", "You might be obliged to", or "You should perhaps", "Maybe you should", "It's possible that you should".
You might ought to apply for the job.
We would say "You perhaps ought to" or "Perhaps you ought to".
They must can feel bad
We would say "They must be able to".