There is a direct train route to Bournemouth, and it has gorgeous beaches!

We go to Brighton a lot because we love it there - takes a couple of hours in the car (I don't think there's a direct route by public transport, unfortunately) if you miss traffic (add another hour if you get stuck in the jams near Brighton!). M40, M25, M23, A23 - dull but serviceable... parking down by the sea front is usually not a problem, and not expensive. Staying overnight can be a pain at weekends as the b&bs tend to have min. 2 night deals. Not impossible though!

The sea is lovely. From land-locked Oxford, your best bet is to head south, or south-west. The closest 'real' seaside town is Bournemouth (1hr 45mins by car down the A34, 3hrs 30mins by National Express 310 coach) which has a 7-mile long beach. Other south coast contenders are Hythe, Hastings (pebbles only) and Bognor Regis.
If you're looking for more, bigger and posssibly less-populated beachfront, a further 2 hours of bus will take you to the 18 mile (and apparently 180 billion pebble, but it's got lots of sand as well) long Chisel Beach in Dorset. Closest point to Oxford is Portland (2hrs 45mins by car, 5hrs by National Express 310 and 305). Make its full length and you arrive at West Bay, not far from the other famous nearby restort of Lyme Regis.
For Craggy Cliffs and rushing waves, you might consider the north Coast of Devon. This is really a car trip, but well worth it. Make your way to the idillic shores of Woody Bay near Lynton (3 hours and 30 minutes by M4 and A39). Be prepared for 500 metres of steep path down to the beach, but be prepared to be rewarded by a place so beautiful you may find it hard to leave.

Good luck, and good beaching.