What should I do if I have accepted an offer informally but am denied the job?
I think the other answer is decent, but OP seems to think that his/her question is not being addressed, so here goes:


  What should I do if I have accepted an offer informally but am denied the job?


Apply to other jobs, of course.


  Does 'a very good position' mean that there is a possibility that I will not get the job?


Anything is possible until you receive and accept a formal offer of employment.


  What should I do if it turns out that I do not get the job in the end?


Forget about that opportunity and start applying for other positions.


  Can I even start applying for other jobs now or should I wait till next week?


You can/should be applying/interviewing for other opportunities until you have obtained and accepted a formal offer.