I used to be the volunteer coordinator for a small homeless shelter a few years back. Most places ask that kids are bit older to volunteer. However, I have a couple of suggestions.
Check with a small, local shelter to see if they need sandwiches made. The shelter I was at had volunteers make about 40 brown bag lunches at home and drop them off at the shelter. A lot of people got a group together to do this. Your child can help make peanut butter and jelly sandwiches, and drop them off with you. You'll need to call to schedule a date and see if they have any food requirements.
You can check with a local battered women & children's shelter to see if they need clothes, toys, etc. These women usually leave home with only the clothes on their backs. A lot of these places offer guest a "store" where they can shop for items when they arrive. You and your child can donate items and drop them off. Talk to the volunteer director and see if you can organize a playgroup. Bring other moms and kids together to play with the children at the shelter for an afternoon. It really depends on the shelter. Some keep their locations private to help keep their guests safe, so don't be offended if they say no.
The Chicago Food Depository is always collecting food donations. I think there is a minimum age to actually participate sorting & packing food at their facility. However, you can buy canned items, or clear out your own pantry and drop off items at your locale Dominicks. Give them a call - you never know.
Good luck - I hope you find something fufilling for you and your son to participate in!