Captain Marvel has always been at his weakest against psychics. The Wisdom of Solomon grants some protection, but against Rachel Summers "some" is not enough.
I think I have to go with Fate here. Any being with quantifiable, physical powers is dead meat to Manhattan - but Fate is a Lord of Order and master of magic, the one thing Manhattan probably can't counter.
Goldfinger. Auric was his own man, not a tool of others, and his plot to irradiate the Fort Knox Gold was actually valid.
Blades a go-go - Sword vs Axe.
Mon-El has one major advantage over Hal - psychological stability. He could get Hal to expend his power ineffectually with a few good taunts.
But even if that doesn't work, Mon is tough enough to take a power-ring beating while delivering a Kryptonian one...which Hal isn't
Power wise, Odin should win. Samaritan has some very unusual abilities though, and his Empyrean Web seems to have a lot more powers than he normally uses.
Heck with it, I'm going with Samaritan.
Herc technically cannot be killed (Olympians in Marvel, unlike Asgardians, are true immortals), but he can be crushed, smashed, beaten, smeared across the landscape...and Manhattan could do all of that in the blink of an eye.