In the US, it's also common to use these among friends:

- See you (pronounced: see ya)

- Catch you later. (pronounced as: catcha later)

- Take care.

- Bye-bye (pronounced very quickly as: buh-bye)

Yes, it might seem a little strange, especially coming from a non-native. The standard use of 'Cheers' is as a toast before having a drink with someone, and the less standard meaning is 'Thanks'. The 'leave-taking' use is actually quite rare, and confined to the situation I described above ie a casual combined thanks-and-bye. As you can see from these comments, there are plenty of other ways of saying 'goodbye'.

'See you!' is also a common informal way of saying goodbye, or 'See you later' if you're likely to meet later that same day. If not, you could say 'See you (+ a reference to the next time you'll meet) or just 'See you soon'.  People often add 'Take care' at the end.

They sometimes do.  In British English, especially among men, 'cheers' has come to mean 'thanks'. So at the end of a short exchange, 'cheers' can be used as an informal, all-purpose way of concluding the conversation before leaving - a casual thanks and goodbye all in one.

I'm from the US and now I usually just say "bye" as do my friends. When I was in school though, people would say things like "see ya" or "peace out" LOL.