Is it correct to say "my ear phones has got tangled in each other"?

my ear phones has got tangled in each other

“my earphones” is plural (even though you may think of them as a single thing), so you need a plural verb: “have”.

“have got tangled” is apparently correct in BrE; in AmE, you must use “gotten”.

“in each other” should be “with each other”, except we have a special word for that: “together”.

So, the corrected version would be:

my earphones have gotten tangled together (AmE)

my earphones have got tangled together (BrE)

Your second example is correct:

we need to untangle them