I am not sure if this was asked before since I don't know if there is a specific terms for this usage.
Is it fine not to put a question mark at the end of a sentence like this?
He hadn't gone to toilet for a week so he told me that he could no longer
resist and may he go now.
You have not written a question per se. The Chicago Manual of Style calls this an indirect question and does not use a question mark.
For example, Martha stopped to pick up a letter from the ground and wondered if she should mail it.
However, Martha stopped to pick up the letter from the ground; should I mail it?, she wondered.
Or better, Martha wondered if she should mail the letter she picked up from the ground.
Simply, She asked herself why
As your sentence is written:
He hadn't gone to toilet in a week, so he told me that he could no longer resist and may he go now.
This sentence you put as a example is rather strange and has a few errors of its own, but I will answer your question, this sentence appears to be a run-on sentence if I'm correct, in this case I recommend rewriting it or removing the "and" by putting a comma or semicolon in place of it. If your looking to keep the sentence the way it is, then you will need to put a question mark as well.
It should look something like this after editing it(corrections included)
He hadn't gone to the toilet for a week, so he told me that he could no longer resist, may he go now?
