I use chopped onion, garlic, carrots, celery, and others in several recipes each week. Can I prep these items ahead for use later in the week?
Definitely yes. Although onions are best done at the last minute. Just be sure to put your mise en place in individual sealed containers and refrigerate until you are ready to use them. A full week's time might be stretching it but say Sunday to Wednesday or Thursday should be fine.
I'd hold off on the garlic too-- all of these items will oxidize and lose quality to some extent, but alliums(which also include shallots, leeks and the like) go bad pretty fast when exposed to air.
Interestingly, I've recently been buying peeled garlic and mincing in the food processor to store in glass jars. Adding good olive oil to cover the minced garlic keeps air out. Assuming I'm adding the garlic to a recipe for cooking, the olive oil blends in.
Bob be sure to refrigerate the oil and garlic. You have created a happy environment for botulism, so also use the oil quickly or only for cooking.
Storing garlic in olive oil is a good recipe for botulism, as Susan notes. http://cooking.stackexchange.com/questions/9451/botulism-garlic-cold-pressed-olive-oil-and-mason-jars (scroll down). If you heat the product and add an acid, the risk is reduced. Better and safer to simply mince your garlic just before you use it.
I always have carrots & celery ready to go because even if I don't cook with them, it becomes much more likely that we will snack on them instead of less healthy things. And, when there is no preparation involved for a snack it makes it even more likely that they will be readily consumed.