I am currently on L1. I wish to change to H1 and move to a different employer. From my understanding, I can only apply for H1 Apr 2016 and it will be approved in some weeks. I can only start to work by Oct 1 2016. Lets say if it is approved my May 2016, can I resign my L1 job and move to my home country and come back on Oct 1 2016?
You most definitely can, but you'll need to apply for a new H1b visa to come back.
Usually, if you're already in the US the H1b application will include AOS (adjustment of status) and not consular processing. So you'll need to explain the situation to the prospective employer to fill the forms accordingly to request consular processing in the consulate that covers your area in the home country.