I was using a damp towel, but I was wondering if there's any kind of homemade solution that would work better than just water on the towel. I won't use fabric softener sheets.

Take your dog to the back yard and use a hose to spray on him then grab an old oversized beach towel and wipe him down with it

You can put baby powder on the dog and then brush it out really well (dry bath), it will prevent a damp dog smell. The baby powder should cling on to the dirt, so you can brush it out.

I use a spray from the store. You spray it on and wipe the dog down with a dry towel. It makes your dog smell really good. Last time I did this before I took him to the vet and the vet thoght the just had a bath.

Fill your kitchen sink with warm water and add in a cup of vinegar and 1/4 cup of baking soda. Soak the towel in that and rub down. You can also add in tea tree oil drops if you have skin issues.
Works fantastic!
You need to look at the diet if you are having smelly dog issues. Cheap foods with more then 2 grains listed in hte first 5 ingredients make dogs stink because it is un-natural for dogs to live a life on cereal. Instead of masking the problem with to many baths, fix the problem at the core.. The diet!

Unscented baby wipes (off-brand is fine). They are cheaper than theose grooming wipes for pets, and do the same thing.