Any of the above will work just fine, as will Power Attack and swinging hard enough. A key tactic to damaging a construct is to stay away from it. Hit it from a distance, or hit it once -- hard -- then quickly move to a place where it can't see you or can't go. You can go away, heal up, then come back again.
It's a mindless construct, limited to its programming. So it will repeatedly fall for the same tricks, like summoning a horde of critters to distract it, and while it kills the critters, your team damages it. When it runs low on targets, retreat, letting it kill the last summoned critter. Then come back the next day. Repeat until it's dead.
Or Dancing Lights might do the job for you, too. There's no saving throw or spell resistance. It's not an illusion. Constructs are so dumb that they can't "figure out" that they're swinging at nothing. The construct might swing away at the "faintly glowing, vaguely humanoid shape" for the entire 1 minute duration while your team hits him repeatedly.
Your biggest advantage against a construct is your brains.