On the phone you say, "please hold". That's very polite. If you say "hold on" or "hang on" on the phone, that would be very casual...you're probably good friends with that person (or maybe just rude).

b. - But people would understand if you said a.
If you said 'wait' then it would not be followed by 'on'.
And 'try' is more of a suggestion to do something (another verb if you like) - so wouldn't ever be used in this context :)

As for Hang On vs Hold On, there isn't much funtional difference. If you imagine it physically, you can hang OR hold on to a bar/cliff edge  (but hanging on normally implies you are suspended).

The best example would be to imagine you're a coach for an athlete (e.g. tennis player). if they're struggling in a match then you would shout 'HANG ON IN THERE, YOU CAN DO IT!', as a more common, colloquial phrase.

Also.... I guess a coat can hang on a hook/peg, but it can't hold on. a person can hang on one while they're asleep, but have to be awake to hold on - so hold on could be more 'active' while hang on is more 'passive'..?

ANYWAY, I hope that helps somehow and isn't too complicated! :D

Yep, I know. But the best choose:

when i called Tim, his sister asked me to ... on for a minute because he were busy talking to someone slse
a.hang
b.hold
c.wait
d.try

When you are talking on the phone it means the same thing.