The biggest problem with the back-to-back sequels is they were intended to be one film until co-director Lloyd Kaufman, upon realizing they had shot too much footage, had the brilliant idea to split the one movie into two. (Troma's recent Return to Nuke 'Em High Vol. 1 seems to suffer from the same decision, which was allegedly suggested by Kaufman's friend, Quentin Tarantino.) Instead of leaving the excess fat on the editing room floor, there's a ton of padding in between the stuff we all wanted to see.
And don't get me wrong: a lot of the stuff we wanted to see is present, albeit smothered. The first sequel opens with a hilariously stupid fight scene before the promising pace is abandoned for an overuse of voiceovers and an absurdly extended interlude in Japan. It's rather like having to sit through Melvin's vacation footage and only one of the two fights there is any fun. A lot of the footage that's used in Toxic Avenger II will later be recycled for Toxic Avenger III, sometimes with replaced dialogue, sometimes unaltered, but always at the expense of us—the audience—groaning.
In other words, there's a good movie between the two. If a skilled editor hasn't made a supercut yet, here's a prime candidate. I haven't even touched upon the fact there are too many versions of the film and the director's cut I purchased more than a decade ago somehow isn't the definitive one.
When I was younger I preferred part II because I actually liked that stuff in Japan, but now that I'm older it's clear the third film, The Last Temptation of Toxie, is the better picture. Like the end of the previous film, the opening of part III was obviously shot after Kaufman decided to split the film into two. The fight may not be as long and complex as the one which opened the previous movie, but its brevity helps establish the pace a little better and believe me: this movie can use all the help it can get.
Toxie's romance with Claire (even Kaufman has stated he doesn't know why they changed the character's name from Sarah) is unexpectedly cute for a movie like this. Toxie literally sells his soul to pay for the operation to restore her eyesight—and get his mother a microwave oven. That's our little Melvin, a selfless darling, and we can only hope the needless Hollywood remake will repeat those aspects of the franchise rather than focus only on the goofy stuff.
So how do the sequels compare to the original? Do you even need to ask? Nothing in these films is half as funny (or downright wrong) as the punks who squash a little boy's head with a car before beating an elderly woman to death. Nor is the dialogue quite as poetic as, "I've always wanted to cornhole me a blind bitch!"
Unless you're a completionist, or a die hard Troma fan, it's perfectly acceptable to skip these sequels. But there is some of that old magic there. It's just in short bursts, few and far between.