Well, actually the militia could have had hand grenades, as they were in use in the 18th Century (that's what the "British Grenadiers" threw). They were unlike the "Mills Bomb" model or the stick grenade, being hollow iron balls filled with powder and a fuse which had to be lit by hand ("modern" grenades have automated that part).

Possessing them, however, is another story. It would be equivalent to possessing a pipe bomb and the BATF, the FBI, and other police agencies take a VERY dim view of unauthorized possession of explosives.

To possess an AK-47 is not against any Federal law UNLESS it includes the fully automatic capability. THEN you'd better have a Class III Federal license. This is true for ANY weapons with full auto capability: BARS, Tommy guns, P90s, HKs, AK-74s, M-14s, M-2s, M1919A6, Lewis guns, Maxim guns, MG42s, M-60s, etc.

Nor can you own a Stryker or Street Sweeper type of shotgun with a permit. Sawed-off shotguns and rifles with barrels under 18 inches long are also prohibited with said permit.