I commute almost 20 miles each way, 7000+- miles a year, and don't have access to showers at work. I hang my often completely sweaty clothes on the door of my office and nobody minds.
THE TRICK (for me, at least): shower before you ride in and always wash your cycling clothes as soon as possible after getting home. You will get sweaty, salty, and sometimes a bit dirty, but not stinky with BO. Arriving at work, I change, hang my cycling clothes on hangars to dry, wash off my face in the bathroom, dab an extra swipe of deodorant, and get to work. Gloves and shoes get put on a boot dryer at the end of each ride to dry out the sweat before bacteria can grow and stink them up (I have one at work and at home).
The biggest source of smell for me is my backpack. I cannot wash it every ride, so it's straps and back-pad get removed and soaked in oxyclean every few weeks when I start to detect a musky smell.
Hope this helps. -Ben