First to correct your question. It should be "What is the difference? When should I use each of these?"
Other - different from the one; in addition to; the remaining one of two. "Not this one, the other one."
Others - pronoun meaning in addition to. "The others in the group" "Three of the boys went swimming. The others went to ride horses."
Another - one more; one different; or one similar to. Examples: "I want another cookie please." "We are going to another restaurant, this one is not good enough." "Tomorrow is another day,"
Else - different from or in addition to the persons or things mentioned. "What else do you want?" "She left with someone else." "That bag belongs to someone else."
I hope that this helps you.