I have a few new Husquarvana hatchets. They do not have any oil on them. In the past I used tung oil just because I have a can. Is that OK, or should I use something else?

it's OK.

I use Huberds shoe grease. Heat it up with a torch or let it sit in the sun on a hot day and rub it in for a couple coats. If the grain pops up under the torch i sand it down, ends up with an awesome waterproof and god looking handle.

Will work fine, I am somewhat lazier in that I just drop my axes in a container (length of six inch pipe) full of raw linseed for a few days every six months.

I pretty much do the same thing but I'm even lazier......I only treat em about once a year.

I use a 50/50 mixture of mineral spirits and BLO.