I've written software with significant amounts of overloading, and lately I regret that policy. I would say this:
Only overload operators if it's the natural, expected thing to do and doesn't have any side effects.
So if you make a new RomanNumeral class, it makes sense to overload addition and subtraction etc. But don't overload it unless it's natural: it makes no sense to define addition and subtraction for a Car or a Vehicle object.
Another rule of thumb: don't overload ==. It makes it very hard (though not impossible) to actually test if two objects are the same. I made this mistake and paid for it for a long time.
As for when to overload +=, ++ etc, I'd actually say: only overload additional operators if you have a lot of demand for that functionality. It's easier to have one way to do something than five. Sure, it means sometimes you'll have to write x = x + 1 instead of x += 1, but more code is ok if it's clearer.
In general, like with many 'fancy' features, it's easy to think that you want something when you don't really, implement a bunch of stuff, not notice the side effects, and then figure it out later. Err on the conservative side.
EDIT: I wanted to add an explanatory note about overloading ==, because it seems various commenters misunderstand this, and it's caught me out. Yes, is exists, but it's a different operation. Say I have an object x, which is either from my custom class, or is an integer. I want to see if x is the number 500. But if you set x = 500, then later test x is 500, you will get False, due to the way Python caches numbers. With 50, it would return True. But you can't use is, because you might want x == 500 to return True if x is an instance of your class. Confusing? Definitely. But this is the kind of detail you need to understand to successfully overload operators.