  Embeddings among fractional Orlicz-Sobolev spaces with different smoothness
are characterized. The equivalence of their Gagliardo-Slobodeckij norms to
norms defined via Littlewood-Paley decompostions, via oscillations, or via
Besov type difference quotients is also established. These equivalences, of
independent interest, are a key tool in the proof of the relevant embeddings.
They also rest upon a new optimal inequality for convolutions in Orlicz spaces.
