irradiated marked men gain strength and substantial health regeneration from radiation. brilliant statement, i know. typically (if not always) there is a warhead or radiation source nearby. you have to destroy the warhead or lure them out of the irradiated area. or else you have to hit them with some serious firepower.
i usually go with brush gun (medicine stick if possible) with some hand load rounds. it will do more damage than the anti material rifle with stock rounds and brush gun/medicine stick have a higher rate of fire. have you tried stealth attacks? i've also had good success with the riot shotgun and slugs. it will take a whole magazine, maybe two, but they will go down. vats headshots are effective especially with a high critical build. i haven't tried the avenger mini gun, but seeing as how it will destroy just about everything, i would think irradiated marked men wouldn't be too different. 45 submachine gun with hand load is rather formidable as well. as is the light machine gun (with hand load of course).
my typical LR loadout is: medicine stick with hand load rounds, riot shotty with slugs, light shining in darkness with hand load, AMR with hand load.
reading your level and weapons of choice, i'm surprised they are not dropping. my guess is they are regenerating health too quickly.
i only play on hard/hardcoe.