Closing cards won't affect your AAoA (average age of accounts), AoOA (age of oldest account), or AoYA (age of youngest account) until a card drops off your report. Credit Karma shows your "average age of open accounts." That's misleading because both FICO and VantageScore include both open and closed accounts when computing age stats.
The closures may appear on your report quickly. It's difficult to tell what might happen with the AU and AAoA. It seems like it's mostly a wait and find out scenario. My best guess is that if the card counted toward AAoA when it was open, it'll likely count as long as it stays on your report. Someone else is better qualified to address what to expect with the AU and how it appears on your credit report. 
@Anonymous wrote:
Good riddance, right?! I'm down to 4 cards and still contemplating closing another 1-2. You just feel lighter and there is less weight on your shoulders! Less chance of over spending or identity fraud etc etc
I'm all the way down to 16 now! 
I want to reduce it even further, but there are a few I have to keep open due to balance transfers, utilization padding, etc. I could close 2-3 of those, but they'd have a negative impact on my wife's score, so they'll unfortunately have to remain open until we've paid down some of her other cards.
Not what I would have done but if it makes you happy and you are willing to take the hits then perhaps the piece of mind is justified. You should remember that "Available Credit" is a part of your score so as soon as the closure reports the points will go down. The catch is by how much and that is where things get fun as you already have a lot of available credit so it might not effect you as much as say someone that only had a few 5k trade lines. I hope that the Sunoco had a second card applied for close after as that way your Oldest card will not slide too much.
