I wish I had seen these posts before. I watched them in broadcast order and it was garbage!
Still got a few laughs though.

I just watched season 9 as well and came up with a sequence of the episodes that I think flows better than the syndication order posted above. But I doubt there is a "perfect" order because some of the episodes have elements that conflict with other episodes - there must have been some serious time and budget constraints when they filmed this season! To me, this season wasn't as bad as it was made out to be, especially the plot lines involving the original characters. Mr. Wick re-opening Winfred-Louder and Lewis shacking up with Kellie's mom were particularly funny.
16. Girlfriend, Interrupted
19. Burning Down The House
20. Liar Liar, House on Fire
3. Foos Rush In
17. Straight Eye for the Queer Guy
21. Sleeping With The Enemy
22. Assault With a Lovely Weapon
18. Still Life With a Freeloader
4. Drew Thinks Inside The Box
10. Drew's Best Friend
2. Eye of the Leopard
5. At Your Cervix
6. Sealed in a Kiss
7. Baby Makes Stress
9. No Booze For Drew

1. Drew Hunts Silver Fox
2. Dog Soup
3. Michigan J. Gus
4. Arrivederci, Italy
5. Asleep At The Wheel
6. House of the Rising Son-In-Law
7. Baby Face
8. Love, Sri Lankan Style
9. The Passion of the Wick
10. Knot in the Mood
11. Finale

I've been binge-watching the series this summer, and I was about to start S. 9, when I saw this.
I let it stack up on my DVR, and watched it in this order. It was bad enough as it was, so watching it out of order would have been awful.
I agree with everyonethe show should have been put out of its misery long before this season.

ABC did a three-year renewal after season 6, and in the first year of that deal, the ratings hit the toilet. They then decided to basically burn off the final two seasons in the summer, and with the episodes out of order. It was really weird at the time. Not that the ratings sank quickly - when Christa Miller left, that killed it for a lot of people - but that they aired the episodes out of order.
The last two seasons weren't very good, but I remember an interview that Drew Carey gave at the time. He said that ABC basically ignored them after the midpoint of the 8th season, so they decided to just do whatever with the scripts and plot lines. If you look at Season 9 as an experiment, then maybe it's better.
I think ABC aired them out of order because Season 9 was sort of cut up into different small story arcs.

Originally aired that way, because at that point ABC hated the show and the cast and just wanted to burn through the episodes and be done with it.
From what I've heard, ABC actually signed a rather stupid contract on their part, years in advance, that demanded they air the show. They'd wanted to cancel the show after Season 7 or during 8, but couldn't. So, that last season, they pushed back airing as long as they could (into the Summer), and just ran them willy nilly.

Was it originally aired out of order, or just in syndication? Why would they air them like that?

Season 8 ends with Drew and Lily splitting up, and him getting close to Kellie.
Season 9 was shown out of order.
Correct order:
16. Girlfriend, Interrupted
6. Sealed in a Kiss
19. Burning Down The House
20. Liar Liar, House on Fire

1. Drew Hunts Silver Fox
2. Foos Rush In
3. Straight Eye for the Queer Guy
4. Sleeping With The Enemy
5. Assault With a Lovely Weapon
6. Still Life With a Freeloader
7. Drew Thinks Inside The Box
8. Eye of the Leopard
9. At Your Cervix
10. Baby Makes Stress
11. No Booze For Drew
12. Dog Soup
13. Michigan J. Gus
14. Drew's Best Friend
15. Arrivederci, Italy
16. Asleep At The Wheel
17. House of the Rising Son-In-Law
18. Baby Face
19. Love, Sri Lankan 5tyle
20. The Passion of the Wick
21. Knot in the Mood
22. Finale
    Winfred-Lauder went bankrupt at the end of Season 7. Season 8 starts with the store property being bought by a new Internet store, and Drew ends up working there.
    They weren't really any stupider, considering previous seasons, but Lewis lost his intelligence after the first season. I suspect DrugCo. They always were of very wrong morals.