Here is a link with some good articles on oils and oil finishing.
http://www.wwch.org/Technique/Finishes/Finishing.htm
These days the "boiled" linseed probably isn't literally boiled, but has had metalic driers added to it to speed its setting. Boiling linseed can be dangerous as the boiling point and the autoignition point are the same.
I don't know if you can get it there, but Terebene is used to help old paint and oils to set. Its handy stuff if you want to make your own oil finish.
Danish Oil is a mixture of thinners, oils, varnish and driers. It will penetrate fairly easily, and sets faster and more easily than plain boiled linseed. The problem with setting oils is that once it has set, additional coats can't penetrate into the wood. If you want deep penetration you have to keep it wet for a while.
I like Tru-oil, but its hard to keep it without it drying out. If you aren't going to use a lot, don't remove the foil, just poke a hole in it, the lid it comes with isn't remotely airtight by itself.
For your axe handle you could use multiple coats of Danish oil, or boiled linseed, or a mix of boiled linseed, beeswax and terebene. If it is true refinishing from bare wood, I would either use the Danish oil as a base, or thin the others with some white spirit to help it get into the wood. Don't worry too much, on an axe you won't need to worry about as many things as if you were finishing a nice bit of walnut for a knife or rifle.
Best of luck
