Just so we have a complete picture here: all of the other answers I've seen describe a type of postdoc which is common in Europe (I'm not really sure about the rest of the world), but unheard of in the US. In the US, basically any postdoc will fit into the standard academic calendar (with a few exceptions that are 1 semester); sometimes you can have flexibility about starting a year later (this is actually quite common with tenure-track positions).
I think the generally accepted standard in the US is that you should only accept one job in a given year (i.e. if you accept one job, you shouldn't just drop it and take another one a month later), though I think people violate this rarely enough that I'm not sure we have reliable data on how it really affects one's career. I think it's generally considered fine to look for jobs after that (say after 1 or 2 years of a 3 year position).