Hi,
My H1B Visa is expiring on 30th Sept 2013. Can I fly to US after filing for H1B exempt? Also, once I have entered US, and if I have already filed for H1B extension or exemption before my I94 expiry, how long can I stay in US after my I94 expires before getting my petition approved?
If you plan to travel after Sep 30, then your cap-exempt petition needs to be approved. You also need a valid visa stamp when you travel to US.
If you plan to travel prior to Sep 30, then you can go on current petition and unexpired visa stamp only if the employer wants you to travel. In this case, exempt petition needs to be filed along w/ I-94 extension soon after you land in US. This will allow you to stay in US for up to 240 days or H-1 denial date (whichever is earlier).