How to find a good contractor? Might as well ask why we are here. Can't
help you.

The utility's explanation is possible. Only problem is that in order to
have overvoltage in someplaces you must have undervoltage in others. Did
you find that? If not, then you don't have a loose neutral. With correct
circuits your 120v circuits are 120v hot to neutral. With a loose neutral,
you have no 120v circuits; they are all 240v, but half the circuits are in
series with the other half. If everything balanced it would not matter, as
all devices would see 120v. But it is rarely balanced. Then the two halves
see different voltages; if you see 139v on one circuit, you will see 110v on
another; and 170v on one and 70v on another. The math is very complicated,
but you get the idea. So, do you have some bulbs that aren't as bright as
they should be, or some outlets that read too low?

Reason I am suspicious is that, while it is not impossible for some the
circuits to have exactly the right voltage with a loose neutral, it is
unlikely. (Now it is possible to have a smaller problem, a loose neutral on
a multiwire circuit. Then only two circuits would be affected; one would be
overvoltage and its sister would see undervoltage, but you would still have
undervoltage. That is a much easier problem to fix, but from your
description you have a more extensive problem)

I hope either you or they checked both legs at the breaker box; they should
be 120v (plus or minus 5%). Don't measure at an outlet, measure from the
screws on a breaker to ground. If you aren't comfortable doing it, then you
shouldn't; but somebody has to. (It is exactly as dangerous as measuring at
an outlet, no more-no less, but it feels more dangerous.)