If you want to be imprecise: they're all the same age, born in the same year. They were 8 from seasons 1-3 and have been 9 since season 4.
But if you want to be exact--who is oldest by even a few months--that's quite complicated. The birthdays of the four boys are as follows:
Kenny: March 22
Kyle: May 26
Cartman: July 1
Stan: October 19
Immediately, you'd assume that this would make Kenny the oldest, but no, not really. Because remember: they're all always the same age. Which means that the years they were born in would vary depending on which episode is going on.
In the episode "Summer Sucks" from season two, for example. It clearly takes place on the fourth of July, which would mean everyone has had their birthday this year except for Stan. But they're all supposed to be 8. Which would mean that Stan would have had to have been born a year before Kyle, Cartman and Kenny. Making HIM the oldest.
But to contrast that: all the Christmas episodes obviously take place on Christmas. Meaning all four boys have had a birthday that year. If Stan had was born a year before the other three, he would have to be 10 or 9, whereas they would still be 9 or 8. But that's not the case; they're still all the same age. So on Christmas, Stan is the youngest.
And in the April Fools Day Prank episode, at the time, Kenny would have been the only one to have a birthday that year, which means that the other three had to have been born a year before him, making HIM the youngest instead of the oldest.
So in other words: whichever one is the oldest changes every time one of them has a birthday.
Or in other other words: they're just the same age! There's no way to be exact.