This is what I do, there are other methods available, but I ride on millstone grit bridleways and therefore have a vested interest in getting it all clean properly.
There aren't any shortcuts really, but it results in a nice clean drivetrain with acceptable wear levels.
My clean chain is lubed with Finish line Dry Ceramic lube. It ain't cheap, but then you don't use much to start with. After a ride I take the wheels off and get the bike in a bike stand. I hose off the thickest mud using a hose with a garden nozzle attached. I have to be careful around the BB, but otherwise water isn't going to get in the wheel bearings 'cos they're the other side of the garage...
I then use a sponge and bucket with Turtle Wax car shampoo to sponge the bike clean, and rinse it all off with the hose. I then use a nylon washing up brush to detail clean the mechs and scrub along the chain which removes what grit and grime adhering to the dry lube (which often isn't all that much) Another rinse with clean water and then I leave the bike to drip dry (or lovingly dry it with a teatowel.... just don't tell Mrs Cube)
I clean the wheels and hubs over a bucket using the sponge and nylon brush to clean the cassette, again, making sure not too much water gets inside the hubs, but they're Hope sealed cartridge bearings with plenty of waterproof grease in them anyway.
With the wheels back on the bike I use a rag and a squirt of GT85 to get the water out of the chain and then relube with dry wax, dripping a drop onto the inside of every roller as I backpedal. I then run the chain a few revolutions to get the wax through the whole chain, then add a drop of the lube to a clean rag and run it over the chain again, this time doing the Mr Allen's Proprietary Efficacious Championship Chain Lubrification Methodology.
I have tried chainsaw oil and found it far too sticky. With dry wax not nearly as much grit adheres to the chain, which is why you can simply clean it with a sponge and car shampoo.
especially in combination with chainsaw oil 
