1/ Listen to the Brandenburg Concertos. Hear the lines as they appear to come to an end, but then don't and go on again, and again. Unlike Mozart, who ties each cadence in a pretty little bow, Bach staggers the endings between instruments for just the purpose of adding asymmetry and disguising the endings. Lots of examples throughout.
2/ Write in 2/4 time as opposed to 4/4. 4/4 will force symmetry on you. It's hard to get away from it. 2/4 lets you slice and dice your lines with greater freedom. 2, 3 and 4 beat phrases are capable this way without changing meter.
3/ Listen to Stravinsky's l'Histoire du Soldat, the opening march. Strong and weak beats are cleverly disguised. Text book asymmetry.
I will be posting a Rondo soon which demonstrates this in my own style.