Rudder blade and centreboard maintenance

I have recently acquired an Escape Captiva dinghy that I am touching up with a few small, routine maintenance jobs. I have disassembled the rudder and (wooden) tiller from the metal attachments and am about to strip off the old and partly degraded varnish using a chemical compound, hot-air gun, scraper and assortment of electric sanders as required. The wood itself is in excellent condition and undamaged. The rudder blade appears to be a hardwood with a good grain and very few nicks and blemishes. Likewise the wooden tiller. Can your readers advise how I should treat the wooden parts when I have sanded them to the best possible finish I can achieve? Polyeurathane varnish? Expoxy? Or just a suitable oil?

I wouldn't strip off the old varnish if possibly avoidable, since you'll stir up the grain and make a lot of extra work. Just sand back to good varnish, don't use chemicals or heat unless varnish comletely shot.
I reckon Polyurethane varnish is as good as anything. Epoxy needs to be coated with varnish to protect from UV so little point in using that you're just spending more money.

A coat of epoxy before you start varnishing will help stabilise the wood and probably add a bit to the life of the varnish.  Not sure if this is cost effective in the long run, but for a some extra work now you can probably add a couple of years to the re-varnishing interval.

Just be aware that epoxy can react with some varnishes so unless you know what is on the blade be careful as you may end up making more work for yourself.

When I did my daughter Mirror I used 2 thinned coats of varnish (really thin, around 50%) so it soaked in and helped seal the surface before the final topcoats were applied. 

If its been on for ages its probably inert and you could put practically anything on it. Ive had reactions with two pack paints but never, ever varnish in 20 years of messing around with boats.