Not sure why your clothes would get oily gunk on them while riding...but ok. Wax is a poor lubricant, sure it keeps the chain clean but I would rather have it last longer.
And is your a die hard wax man and just have to wax your chain the drip kind is the worse; the best way to wax a chain if to use paraffin wax with a bit of teflon oil mixed in (Slick 50 or the such). You take a block of wax and put into a can big enough to hold a rolled up chain, put in about 2 or 3 tablespoons of the teflon with the wax. Then get a pan (an old pan you don't really want to use for food anymore or else your wife will fry you) and place the can in the center of the pan with about 2 inches of water in the pan. Heat the mixture on the till the water just starts to boil then turn it down i bit, Don't let it get too hot because you are heating oil, I let you ponder what might happen if it gets too hot! After the wax and oil has completely mixed together take it off the heat and let it solidify.
Prior to doing the above remove the chain off the bike and clean it, doing the hot wax treatment will clean the chain some more but it's best to preclean it, then roll the chain up and wrap a wire around the chain to hold it together but also so you can crab it with a hanger or pair of pliers later when it will be to hot to handle, and place it in the can with the wax. I like the coat hanger because you can grab the chain and hang the hanger on a hook without touching the chain. Then set the can back into the pan and add more water to bring the level back up to 2 inches as before. Bring the water back to boil and wait for the wax to melt into a liquid state, then stir the chain around with a wood spoon (again not going to use for food later), let it cook for at least 20 minutes because the chain and the wax have to bond, but keep moving the chain ever so often. And never leave it unattended while cooking.
Then remove the chain with pliers or a coat hanger and don't touch it because it's very hot and it will burn you good. Let the chain hang and let the wax drip into a paint pan but don't shake it while it's dripping and cooling. Once the chain had cooled to the touch then your ready to reinstall the chain. No need to clean the excess wax off because as you ride it will flake off anyways. If the wax starts to build up on the gears just pour some hot water on it and it will come off.
That is the best method, this wax crap in a bottle does not do the job anywhere near as good as the above. And the best way to do the hot wax is to use 2 chains, so you can have one chain waxed and ready to go while your doing another. The hot wax treatment was the way it was done for many years by many cyclists including me until bottle wax came along and everyone wanted to wax it the easy way, problem with bottle wax is that it's only good for about 60 to 70 miles then the chain starts making noise and once you hear noise accelerated wear has begun; also liquid wax in a bottle needs to be put on a chain and allowed to sit overnight before riding. And remember too that wax is best for relatively dry, clean climates and on bikes that aren't ridden in the rain or get wet.
Here's a Sheldon Brown site that tells about the effectiveness of wax as a lube:
Chain Maintenance
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