Bad cuticles and hangnails, help?

I realize there's a thread similiar to this, but my situation's different.

I've never bit my nails in my life. But over the few months, things have gotten pretty bad: my cuticles are really long, I mean a few centimetres long, and I am getting painful hangnails.

My questions are:

How can I get rid of these hangnails?
How can I stop my cuticles from growing any longer, and get rid of them altogether?

I can't push them back because they're too long, so they just straighten out again.