My H1B has already been approved but its effective date is in the next 3 months.
I want to know if
1. I can quit my job and stay on OPT.
2. I can transfer my H1B to new company before effective date.

1) You can stay on OPT even if you dont' have a job, so yes, you can
stay on OPT and quit your job

2) You can hold multiple H1b. There is no "transfer" H1B per se. The
portability rule enables existing H1B holder to apply for a new H1b
without being counted in the yearly quota, and it also enable the
applicant who is applying for a new H1B of a similar job to start
working without waiting for the approval. So it feels like a transfer.
 In order to use this portability rule, you need 3 months's pay stub
of your existing company/job.

So, if you still have OPT, it would not be a problem for you to quit
your job and apply somewhere else. However, once your OPT expire, and
your H1B has not been approved, you'll be out of status at that point
of time.

The best way is to check with an immigration lawyer. Meanwhile, you
can also check out www.immigrationportal.com's forum