When is it appropriate to use "see you later"?

Solution 1:

Generally speaking, "see you later" is just slang for goodbye. I have heard it used in all of the situations you list in your question. The order you present matching the order I would give them for frequency/commonness.

1. When you will be seeing the person again later that day.
   • All the time.
2. When you will be seeing the person soon (e.g., in a few days)
   • All the time.
3. When you will be seeing the person again at some point in the future (e.g., next year at Christmas)
   • Very frequently
4. When you are suggesting that you want schedule something specific
   • Surely, but it is usually turned into a question: "See you later?" being short for "Will I see you later?"
5. Whenever you say goodbye, regardless of whether or not you will ever see them again
   • Definitely heard it, but it can be awkward, specifically because it isn't correct and you're drawing attention to the permanence of the goodbye. This has been used for comedic effect on stage and screen, to mixed results (really, really bad example: possibly the worst fight scene of all time [Warning: Graphic Violence]).

Solution 2:

I find that the phrase is used in all those situations, except that it always comes across as strange except in the first instance and stranger and more inappropriate as you go down your list.

An alternative that sounds less strange is

see ya!

which works without strangeness in all informal situations even if it is impossible for a revisit.