"Stay / sleep for the night" VS "Stay / sleep overnight"

Question

What is the difference between:

a. stay / sleep overnight
b. stay / sleep for the night
c. stay / sleep for one night

Just in order to clarify what I need, I made up two examples. Please let me know if there is any difference between my suggested choices (to me, more or less they mean the same thing):

1. He stayed / slept at my home................

a. for the night
b. for one night
c. overnight

Or as a sign of hospitality, ask someone to stay at my home for the night and not to go home:

2. Stay / sleep here............

a. for the night
b. for one night
c. overnight

PS. I have read the similar thread: but that was not that helpful that it should be.

Answer 1

These have similar general meanings. Some give additional information that is omitted in others.

So "for one night" is explicit about the number of nights, whereas "overnight" doesn't necessarily imply that you can't stay a second night.

When you stay "stay the night" I'd expect some context to let me understand which night you are talking about. That context may be provided by the situation.

Moreover, these expressions (especially "he stayed for the night") could be understood as a euphemism for "we had sex". But this interpretation is very context dependent.

Stay overnight is the simplest and most useful form

Use "for one night" when you mean "not two nights".

"Stay the night" when you mean to spend the night with me.

A hotel wouldn't need this. It is implied that you can stay overnight at a hotel. You'd just have a sign saying "Hotel" or "Rooms available" or similar.