My H1B expires in May 2004 and I have not applied for extension.
---- You can apply H1 extension 6 months advance of your H1b expiry date. If H1 extension applied it may take 3-5 months for the H1 extension approval and if Extension is filed it is not abandoned if you go out of US, only Change of status like H4 to h1b or L1 to H1 is abandoned. You have valid visa and I-94 if your trip to Canada is less than 30 days you can enter with same I-94.
yet. If I land in the next 1-2 weeks, will such short duration of validity (~3 months only ) cause any problems while returning to the US ?
------- No, you can enter till the date Visa is valid, you donít have any problem just land and come back next day or apply for SIN with HRDC office and provide any friend/relative address for SIN and that will be sent on Canada address to your friend and he can send the SIN card to you in US by FedEx. When land also fill up the form for PR card and provide the Canada address and PR card will be mailed in 4-8 weeks to Canada address and later your friend can send the PR card to you in US by FedEx (request your friend to make copy of PR card or SIN card before he sends because if lost you have the record)
Should I wait till I get h1B extension to land in Canada and return back to the US ?
I donít know the expiry date of your Canada landing paper or permanent Visa. You can file extension of H1 but it will take to get approval notice 3-5 months and that time your H1B stamp will be expired and you may have to revalidate the H1b visa stamp from DOS and it may take again 3 months to get the passport back from DOS and no guarantee that they will stamp the H1B visa. If I am in your situation I will land now when I have H1B visa stamped in passport and after landing I will be back before H1b visa in passport expire.
Remember, I am strictly a layperson without any legal training. Please, if in doubt, be sure to use the services of a professional lawyer whom you trust.