Onward, forward, forth are comparable when they mean in the act of advancing or getting ahead (as in a movement, progression, series, or sequence).
They are frequently used with little or no distinction, but onward often suggests progress or advance toward a definite goal, end, or place.
Forward, opposed to backward, has more specific reference to movement or advance with reference to what lies before rather than back in place (see forward under BEFORE ) or in time or in a succession (as of incidents in a narrative or of steps in a process).
Forth is often interchangeable with forward without loss, but in certain idioms it may be quite distinctive and imply a making known, present, available, or real something previously unknown, lacking, unavailable, or hidden; thus, one brings forth from or as if from a place of concealment and one sets forth by providing or by making simple and clear.