Possibly is more informal. It is an adverb. You use it to describe an action that could take place, or an action that could be true. It implies that it is less likely to actually happen.
Example sentences: "I possibly forgot my keys." "Her name is possibly Karen."
Likely is more formal. It is an adverb. You use it to describe an action that could take place, or an action that could be true. It generally implies that is more probable to take place than possible.
Example sentences: "It's likely she is late again." "I'm likely to drink coffee in the morning."
Feasible is very formal. It is an adverb. You use it to describe an action that could take place, or an action that could be true. It is generally used to mean less likely.
Examples: "It is feasible that I missed a turn."
If you are fairly certain something will happen, use likely/probably. If you are less use, use feasible/possible.