Assuming we're talking about Iluvatar before the 'Old Hope' comes true, his opponents would be thwarted by his complete lack of corporeal existence. On the other hand - okay, let's do this.
Scenario: the history of Middle-earth happened ~6000 years ago. After the Eldar departed forever, the Valar pretty much left the mortal lands to govern themselves. As part of that, a rash of new gods sprang up - how, doesn't matter, they just did. (Hey, it's a crossover! Don't like don't read etc) Said gods run their various classical realms, fade into the background, and recently experience a resurgance due to a bunch of demigods/magicians/people surnamed Chase running around.
Around about, oh, three hours from now, Zeus finally sits down and reads that 'Lord of the Rings' book he's been meaning to get round to. (Actually, the book Hades recommended was Lord of the Flies - 'reminds me of our family gatherings' - but Lord Zeus wasn't really listening). When he gets to the end, he realises two things:
1/ It's true.
2/ That means he is not the supreme deity.
Breaking with tradition, Zeus goes to visit the other pantheons - the demonesque Egyptians in their underworld and/or wanderings, and the Asgardians in... wherever they are, the book's not out yet. Through flattery, argument, and shameless bribery, he convinces them to join him in overthrowing Iluvatar once and for all. "After all," he says, "I did it to my father..."
Round One
The pantheons (panthea?) try to go to the Timeless Halls. Being a part of the world, they can't.
Round Two
The pantheons (pantheii?) try to travel to Aman. Since the Straight Road has long since been severed, and it's not a mystical realm - just Elsewhere - they can't.
Round Three
Set (of course) suggests rounding up rabid Lord of the Rings fans, brainwashing them into wanting to kill Iluvatar, then killing them and - on the principle of 'you get the afterlife you expected', which seems to apply since the Kane Chronicles - getting them sent beyond the circles of the world. The others reject this.
Round Four
Set does it anyway, because he's Set.
Round Five
Iluvatar idly notes that some of his arriving Children are a bit messed up in the head. He asks Manwe what's going on.
Round Six
Manwe and the other Valar have a council. They bicker and get nothing done.
Round Seven
Ulmo (being Ulmo) pops across to the mortal lands to have a look. He runs into Poseidon, and they share a goblet of wine (since it turns out that Poseidon's palace is built on the site of Ulmo's old house, they hit it off immediately; neither of them are particularly prone to vengeance or warlike behaviour in this crossed-over verse). During their chat, Poseidon explains what's going on.
Round Eight
Ulmo heads back and lets Manwe know what's happening. At this point, there are two options.
Round 9A
The Valar point out that mortals are always killing each other, and that - much like Sauron - getting involved isn't their Thing. It's a shame, true, but it'll die down soon enough. LotR fans are driven underground, and the PPC becomes a secret-refuge-cum-guerilla-organisation.
Round 9B
The Valar get seriously upset - enough that (noting as they have before that directly confronting the enemy would risk destroying the world, 'and the Children are kind of using it') they lay down their guardianship of Arda for a time.
Round 10 (only after 9B)
Iluvatar hits New York with a tsunami beyond anyone's imagination, destroying the current site of Olympus; the East Coast of America is under 100 meters of water, permanently, stretching in to the Appalachians. He also hits the original Mount Olympus with a gigantic earthquake, reducing it (and most of Greece) to rubble. To follow up, he enacts a 'change in the world' - this time, he causes the Seen and Unseen worlds to merge, permanently. The Mist vanishes. The Duat goes with it. All the metaphysical domains visited by Greek and Egyptian alike go poof. Transit to extra-dimensional realms becomes impossible. Oh, and whatever the Norse have going on is hit by massive natural disasters and/or the Change.
Result: The remains of the USA splinter, and Western Civilisation falls - which, since that's what both sets of deities have been worried about, pretty much knocks them on the head regardless. Africa descends into universal warfare, what with the lack of incoming relief, trade, or anything else. The Olympus Quake sends massive tidal waves across the entire Mediterranean coastline, so there's no Italy, Egypt, Israel, southern Spain, southern France... you name it, it's gone. The New York Tsunami was probably caused by a mid-Atlantic quake, so the rest of Spain and France also go under, along with most of the UK and Ireland. The Caribbean islands all sink.
Global tensions rise (there's an understatement for you). China is now the dominant power on the planet. Assuming humanity survives (which shouldn't be presumed, what with all the nuclear weapons and suchlike), we'll all be speaking Mandarin.
The Timeless Halls get a whole bunch of new, and very confused, mortal residents. Iluvatar makes them all feel better. Awww.
hS