we will organize a musical event next year.
we will organize a musical event, next year.
Next year we will organize a musical event.
Next year, we will organize a musical event.

Is there any difference among the above sentences or each says the same thing.

I will appreciate if Mgmat can clarify it.

Many Thanks in advance

These are all saying the same thing. (Though note: for your first pair, you should not have a comma. For your second pair, you should have a comma. This test, however, doesn't test us on correct comma usage, so you don't need to worry about that.)

Note that here you have an adverbial modifier, not a noun modifier (what happens next year? we will organize). Noun modifiers must touch the nouns they modify; adverbial modifiers are not subject to this restriction. Adverbial modifiers only have to be placed such that it is clear which verb they're modifying. You only have one verb here, so there's no issue with whether "next year" goes at the beginning or the end.