Keep Off: Not to touch, go on, etc.
Keep off the grass Sara, your father will be furious.

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Keep Off: Avoid eating, drinking certain things.
I am keeping off red meat for a few months for my health.

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Keep From: Prevent.
My flu is keeping me from going to work.

Keep From: Not to tell someone something.
Worried about her reaction, we kept the news of her aunt's illness from her.

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Keep In: Stop someone going out.

I kept him in after school due to his behavior earlier in the day.

Keep In: Stop from being seen.
Despite her anger, she kept it in until he left the room.
 

Keep Up: Work, move, etc at the same speed as someone else.
You must work harder Jones! Keep up with the others.

 

Keep On: Continue.
Keep on going until you see the supermarket.

Keep On: Continue to employ.
I will keep you on for another two months - then I make no promises.

Keep On: Continue to wear.
Keep you shoes on because we are going out again soon.

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Keep To:  Stay on/in a mentioned place.
Keep to the London road for about ten kilometers, then head east.

Keep To: Follow a plan, regulation.
We must keep to the agreed schedule, otherwise we will have problems.

Keep To: Hold someone to a promise.
You promised payment and I will keep you to it.

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Keep Away: To avoid or to not come near something.
Keep away from that old factory by the river. It's very dangerous.