Might be wrong here.

From a orthodox perspective(just reverse left and right)
But a overhand right, is when you step in and to the left as if you are going to weave under a right handed punch, as you duck down and slightly to your left, you throw a hard right handed hook to the head over the opponents guard.

Very different punches, you would very rarely throw a overhand right.
You are also on the inside after this punch has landed.

A right hook can be throw any time but is usually after a jab or left hook.
You remain upright (standing), when the punch is throw and better to finish with another jab or left hook, before you step away.

Over hand right you are on the inside, also need to keep you hands high and close to your head, you head is close to their chest and you are slightly bent over, you want to remain close to the opponent so it is more difficult to counter, you would follow with a left to the body and be cautious when you move away.

You don't want to throw many overhand rights, it is a power punch, and using this many times you become easy to predict.
Its effectiveness comes from its surprise factor.

> Its always dangerous fighting someone in the opposite stance due to the fear of the straight right/left but how about a rear hook or an overhand?

Do you mean a cross.
You can always circle away from their power hand, left against orthodox , right against a southpaw

A good counter for a cross, is a fast jab before the cross can land.
If they are throwing a straight lead(cross without a jab before), punish them by lateral movement(circle left or right) and a fast jab before their punch lands.

If you can win a fight with a jab and a cross(straight rear), the better it is for you as you can block punches more easily and stay out of range from hooks.