It would be legal for you to use your new-old rifle on any big game animal in Maine. Per the regulations
http://www.eregulations.com/maine/hunting/firearms-laws/ :
Deer hunting
No firearm may be used which uses .17 or .22 caliber rimfire cartridges, except .22 magnum. No firearms of any kind may be carried while hunting deer with a bow and arrow during the special archery season on deer and the expanded archery season on deer, except that a person who also holds a license that allows hunting with firearms may carry a handgun but it cannot be used to shoot a deer or dispatch a wounded deer.
Moose hunting
It is illegal to use .17 or .22 caliber rimfire firearms, shotguns using shot loads or a crossbow. Hunters who have a moose permit and are 70 years of age or older or disabled persons who have a special handicap permit to use a crossbow may hunt moose with a crossbow (expires 1/1/2015).
Since there are no limits placed on what may be used for bear hunting, by implication one could take their Marlin 39 out to get a bear. I would not recommend it, but it would be legal.
Similarly, I would not recommend hunting moose with a 22 Hornet, no matter how good a shot one is. Moose skulls are pretty thick. The chances of ol' Bullwinkle making his way into a deep swamp b/c he didn't drop right away and then having to be recovered from in there militate in favor of a larger caliber more likely to drop him in his tracks. Nearer the road. On dry(er) land.
