When I turn the key on but have not started the engine I always get a buzzer warning because the pump isn't pressurizing the oil system yet. Having oil in the bilge is a different issue though.

I'd check the oil filter first to make sure it isn't loose. You don't mention what engine you have (I have a U35BC) but on mine there is a bolt on the front starboard side of the engine; I had a slow leak through that once because it vibrated loose. Then of course you could check the oil pan itself under the engine to make sure the bolts are tight and there isn't a rusted out spot in the pan. I guess you'd have to use a mirror to check that or run you hand around under the engine.

Mark,
Carefully check the condition of the oil pan with a good external examination. They have been known to rust through and seep oil into the bilge. I hope that's not the case with yours and hope it is something simple like a loose filter.
Bill

[quote=SafariC36]I am the proud owner of a Mk1 1984 36 with a universal engine. After one month of owning and sailing, I now have an oil light, and audible alarm that goes off on the key panel when the ignition is in the on position prior to starting the engine....When I start the engine the alarm goes off after a few seconds. ...
[/quote]
That's precisely what is supposed to happen.  The alarm should ALWAYS go on whenever the key is put in the on position but the engine is not actually running, because you have no oil pressure at that point.  I'd be concerned that the alarm isn't working properly if that wasn't occurring in the past.
[quote=SafariC36]
I have also noticed increased oil in the bilge. .
[/quote]
This seems to be an unrelated issue to the first one  (unless you are getting the alarm after the engine has run for more than a couple of seconds). 

But you shouldn't have ANY oil in the bilge, much less an increased amount of it   One, because this could be an indication of a possible leak somewhere, and two because discharging that into the sea via your automatic bilge pump is going to be a serious no-no with the Coast Guard and your local harbormaster (and, obviously, bad for the environment). 

Do you have an absorbent mat under the engine (you should)?  Change it frequently, and maybe you can see where the oil is leaking from.  Have you checked the engine oil level (and the transmission oil level) to see whether its going down?  Or could it be the result of a sloppy oil change (don't ask me how I know)?

One other suggestion about oil in the bilge. Its correct you should have none, but since you do, I take an oil absorbent sheet (from NAPA) and rip it in half, then roll it and wrap a wire tie around it. then I leave it in the bilge in the aft section away from the bilge pump. Any oil or fuel that gets into the bilge gets absorbed and not pumped over the side which is a definite no no.

Are you sure the stuff in the bilge is not diesel? I'd check that as well as it is more common. Al

When I purchased my 1987 I had a clean running engine. Did my first oil change, the following year I had oil in the bilge. Long story short, the PO left me a Fram filter, which had a small crack in the gasket. The little bit that leaks makes a heck of a mess when it sloshes around in any bilge water when on a heel.