LATEX OVER OIL!
Prime with one coat of Glidden Ultra-Hide Gripper.
Wait overnight - then topcoat with your choice of color - Glidden Evermore Satin or Semi-Gloss - Glidden Ultra-Hide Semi-Gloss - Ralph Lauren Satin or Semi-Gloss. I would recommend two topcoats.
All are lates products available at The Home Depot
You will need to sand the trim to give thwe primer something to stick to and this a good practise any time you paint over glossy slick paint. Then you can wipe off with denautered alcohol to remove oils and dirt that get on the surface. Then you can prime with either an acrylic bonding primer such as Zinsser 123 or an oil based undercoater from the paint supplier that makes the finish paint. Then you can finish with an acrylic latex semi-gloss or gloss depending on the look that you want and yes 2 coats will be best.
As I was just saying in another post - I recommend THD a lot - not because I love THD - but because they are the most common supplier of Glidden products - which I happen to know and like.
If you have an ICI Paints Store - a Devoe Paints Dealer - or if you are in New England - and Aubuchon - or just a mom and pop paint store - you should be able to find Glidden ICI products as well.
THD is just the most likely place for everyone everywhere to find the products I recommend.
Having said that - B-I-N 123 is a good product (Gripper is better in my opinion) - I used it a great deal before Gripper was introduced - and it too will work to prime old oil.
5 I agree too,this is why I recomend places like H irshfields (I think Mr.) said he has never heard of this.Also Sher win Williams,M enards,and L owes,I use the spaces like this so it doesn't delete what im typing this board is very biased only liking 1 store,all others mentioned get erased.
Anyhow I would sand it like 5 said,this way you know you are getting the best adhesion possible for your primer to stick to.Sanding will also let you use most any interior latex primer you want to use then being able to put any brand of interior paint on top of this.