Hello jibatma:

as many have suggested, i also suggest you to apply for canadian PR as soon as you can.  getting job is tough everywhere, at least you would nt worry about your status once you get your canadian PR.  in the mean time, do not quit applying jobs, you have to apply as many as you can.  but canadian PR is very very good option for anyone who does nt want to go back to nepal. 

regarding attorney to file green card here in usa, being a phd holder, you can apply for green card in EB1 category.  however, you need to have very good recommendation letters from industry and academics.  how many papers did you publish during your PhD.  if you have strong recommendation letter and good number of publication, you may be able to get green card in less than 6 months.  so, i would sugges you to try both and also keep applying jobs.  i know its frustrating and almost everybody goes through this process, very few lucky ones get things easily but most of us have gone through hard times like you have now.  matter of fact, i dont think you are having hard time, if you get your H1b, your problem is solved.  these things come if you dont get one.  good luck.