Good Boats
The Mk II Oday 23 (the model you are looking at) is a nice boat. I have had a 1979 Oday 23 for over 10 years, and really like her. Things to look for in an inspection specific to this boat:
I agree with Ed; check the bulkheads. On these boats, the shrouds attach to a chain plate that runs through the deck and attaches directly to the bulkheads. If water gets through, it accumulates around the attachment points on the bulkhead, rotting the whole thing. Again, I think Ed is right: if you can't replace them yourself, it ain't worth it to have a yard do it. It will be just too expensive.
Check the deck for delamination, especially around the chain plates, the forward deck vent, and the mast step. Buy a rubber mallet and gently tap the deck to check for voids.
Check the rudder for delamination, especially at the pintles, and check the transom around the gudgeons. Oday was notorious for using undersized hardware here, and stress cracks can let water in. Check to make sure the rudder headstock fits snugly to the head of the rudder and that there is no play there (I mean back and forth, not up and down). This is a high-stress area, and you don't want it moving around.
Check the interior of the transom around the gudgeon and motor mount attachment points. Look for water intrusion and corrosion of bolts and nuts.
Lift up the cabin sole. Is there water in there? The Boat has no stock below the waterline thru hulls, so if there is salt water in there, you have a leak. If there is freshwater in there, it is likely from a leak in the deak or the ports or somewhere from rain water. See if the owner knows where. He may know and just not had the desire to fix the problem.
Look at the water hoses for the internal water system. Are they clean? If you intend to use the system, try and use the pumps at each of the two sinks to make sure they work.
And the "biggest" issue for this boat (in that it is the biggest source of problems): the centerboard. The system is simple and easy to maintain, but sheer age is starting to catch up with these boats. Make sure the centerboard works. It is controlled by a line to the bridge deck in the cockpit. There are no pulleys, cranks or ratchets. The line is attached directly to the trailing edge of the board. It should go up and down easily. Unfortunately, the boards jam in their slot for lots of reasons. Some of the reasons are easy to fix (barnacles in the slot), some impossible (board has become saturated, swollen and jammed). The only way to know is to haul the boat and look. Assuming the board works, see if you can figure out the last time the centerboard pendent line was replaced. Because the shackle holding the line to the board is underwater a lot, I think it should be inspected every year, and replaced about every five years. This number could go up or down depending on how much the boat is in the water.
General issues not particular to this boat:
Does the outboard work? Can you tilt or raise the outboard completely out of the water? If the outboard needs to be replaced, you could wind up spending as much for the engine as you did for the whole boat.
What about the condition of the cushions? Unless you are adept at making them yourself, forget about new ones. Cushions are expensive. For this boat, it will cost you at least $1200.
Condition of sails? "Neil Pryde" was the original sailmaker for much of the Oday 23's. If the sails are Pryde's they are likely original to the boat and in need of replacement.
Ask how old the standing rigging is. If it is more than 10 years old, you should replace it. For this boat, that is several hundred dollars.
Try all of the navigation lights to make sure they work.
Electronics included with the boat: do they work? Are they so old that you hope they don't?
Like I said, I love my Oday 23. It is perfect for daysailing and the occasional overnight with two people. If real cruising or racing is in your plans, I would go with a different boat.
Good luck and let us know what you find.