I'm guessing due to the fact that most cartoons don't have a set timeline like ours, M&T can utilize the 'sliding age' rule alot. Which means, they can age the boys up a year if they like, and age them back a year also.
I don't keep track of the times they've done it (it happens ALL the time), but here's a few bits..
Stan: Established as being eight, then nine in "Biggest Douche". Is back to being eight due to "sliding age".
Kyle: Established as eight, then as nine in "Cartmanland", has birthday in "Casa Bonita" (ten?) then back to eight.
Cartman: One could say that he turned nine in "Damien". He's been sliding back and forth ever since though..
Kenny: Always been eight
As you can see, the sliding age rule is used so that if they age AT ALL, it'll be retconned and the four will be the same age again. Gotta love cartoons! Nothing has to really make sense..

sliding timeline would be a good explaination had they not been permanently slid forward one year to fourth grade. it has been pointed out in interviews and episodes that they are nine.
all episodes you mentioned, except damien come after the switch to fourth (season 5). Stan was in fact, never established as 8 in "biggest douche". first mention of age he says "I'm nine years old". how was he established as 8? he wasn't. No one has been 8 since they moved to fourth. except perhaps kyle, who as you pointed out we don't know if that's his ninth or tenth b-day in "casa bonita". we can probably assume it's his tenth since he say's he's nine in an episode from two years prior. The sliding time rule then went into effect making him nine again (probably) in "all about mormons".
the creators do use the "cartoons don't have to make sense" rule often, but not this time. time does go back to where it was the previous episode in some cases, but this is simply a mistake on someones part.