Is it bad to cut onions and other vegetables on the same cutting board? Does the type of cutting board matter? For example, do wooden cutting boards that are regularly used to cut onions (or other potent veggies, garlic, etc.) start to smell permanently like onions?
No it ain't bad. You would probably not end up in hell for this :-)
It's all a matter of flavor, i don't really mind getting some onion juiced into my next dish, unless i'm making something sweet like fruit salad - in this case i would rinse the board before moving on.
My advice to you about boards is: Get your self a proper wooden or bamboo board or butcher's block, treat it with care (clean it an soak it with mineral food grade oil every now or than...) and that's all you'll even need.
I've been using my favorite board for over 10 years now. And it doesn't smell of onions :-)
Assuming that you'll soon be cooking the vegetables in the same pan as the onions/garlic, you have little to worry about in terms of 'contaminating' the former with the latter.
Softer boards will accumulate scores and grooves from knives which will trap oils and juices from onions and garlic which may eventually start to make them smell. However, it's a good idea to replace your cutting boards every few months anyway to guard against bacteria build up, so it shouldn't be too much of an issue.