According to a comment on this thread:
Bryko614 wrote:In the third film, Andy has two tickets for a concert that was in November 2009 hidden behind other papers and pamphlets on his cork board. So it can be assumed that it takes place in at least August 2010. This would also make sense because his August calendar ends on a Tuesday, which happened this year.
The calendar in Toy Story 2 is in clear view when Buzz and Rex are playing the video game. It ends on a Wednesday, which is troublesome because there were no Augusts ending on a Wednesday from 1997-2002 (the only logical time frame) due to the possible year of 2000 being a leap year. Although apparently the movie takes place on the 15th of August when Andy leaves for camp.
I'm not sure if there's a calendar in the first Toy Story, but if there is then I'm too lazy to check.
Based on this, the movie doesn't match real time closely. So there is no way to be 100% sure of when it takes place, and how old Andy is in 2.