Carbs
 

Besides oatmeal, whole wheat bread, pasta and rice, what are some good slow burning carbs?

Veggies

I would put all the ones you listed as very fast acting carbs. Onions, garlic, Brussel sprouts and the like I would put at medium, and peppers, cruciferous veggies, and green leafy veggies are to me, slow. Check out the GI (glycemic index) if you want specific rates.

That being said, don't put too much stock in it. Get your carbs from veggies, root sources, and if you handle the well, maybe whole grains, and you're set. Stay away from refined sources and you are good to go.

What about celery? Or carrots? Are they?

Check here for others. glycemicindex.

Celery is pretty low, carrots pretty high. As a rule of thumb, think about the portion of the plant you will be eating.

The stalk is usually fibrous and low in carbs
The leaves are the same, but there are exceptions, such as onions, in which the bulbs are actually modified leaves.
The fruit is usually higher, such as in tomatoes or berries
The roots are frequently the highest, especially in tubers like potatoes.