My girls have brought home a range of different invites- two weeks ago my 2nd grader brought a b-day invite home that had the party being in 3 DAYS after we received the invite! We didn't get to go, because of a hockey thing we had, but we still gave the little girl a gift, because my daughter is good friends with her.
My kinder. daughter brought home an invite WAYYYYYY too far in advance- the party was 6 weeks away!
I don't think that there really is a 'normal' we've gotten most of ours around 1 1/2 to 2 weeks in advance, but I don't really mind either way- because we have our 'month schedule' usually set by the beg. of each month (we have hockey trips planned, and we as a family SCHEDULE one weekend of doing NOTHING- which we spend as a family doing things around home or we go skating, to a movie or what ever)
After Christmas every year, I buy clearance gifts for different ages- 75% off of a $20-$30 gift is nice! That way my girls can bring nice presents, AND I don't have to rush out and get somthing every time we get a 'last minute' invite to a party! It saves us money and time. I have a 'gift' section in the top of my closet.