I think it has to do with asymmetry in direction during emission of decay products .also what is implied physically when we say parity is violated in beta decays? I cannot imagine 'l' having an odd value can take the particle in a different trajectory. Please clarify using the example of beta decay if possible.
I would like to write a long answer, but almost all the information I think you require can be found here: Wu experiment.
Whilst I'm reluctant to link Wikipedia, this page contains details about how parity is conserved in strong and electromagnetic reactions, but not in weak ones.
Physically what is implied when parity is violated in beta decay, is that the bosons involved in the weak interaction (the interaction involved with Beta Decay) only interact with certain types of matter, and certain other types of anti-matter. Hope this isn't too hand-waving and general, I just don't want the answer to get bogged down in other matters. If you want more information on that, read the above article.
This question is highly interesting in terms of leading into reading about CP-violation nuclear physics on the whole.