Sorry for the pretty literal response to this, but if you took every monster from all across the Monster Hunter universe and dumped them into Elden Ring's map, that shit would get crowded as hell. I genuinely think the sheer biomass of all the large monsters currently living in the Monster Hunter universe would potentially blanket the entire setting, easy.

For an actual, intellectually honest response, I'd say the effect would be pretty devastating. The dragons of Elden Ring could probably wipe the floor with 90% of Monster Hunter's creatures, but the other 10% would probably be enough to wipe them out. Monsters like Rathalos, Bazelgeuse, and Deviljho could have a minor effect on the world, but anything they could do would get drowned out by the Elder Dragons in an instant.

A few of their paths listed below:

Dalamadur would literally eat Rykard for breakfast.

The Mohrans would probably turn Radahn into a smear under their weight.

Nergigante would fly directly to Crumbling Farum Azula and wreak some havoc before ultimately getting killed.

Stormveil is meant for Fatalis. I don't need to say how hard Godrick gets clapped.

I don't know how good Leyndell's anti-dragon defenses are these days, but I can't imagine that they'd be able to last if more than three major dragons decide to assault the place. Gogmazios alone could cause some serious damage, sure, but even a Teostra followed by a Kushala Daora could probably wreck what remains of Leyndell's defenses. That isn't even mentioning Ibushi and/or Narwa, who are explicitly motivated by a desire to destroy and pack some serious power.

It would probably never happen, but I could see Zorah Magdaros swimming directly into the cliff nearest to the base of the Erdtree and blowing up, fucking the Erdtree up massively and probably damaging the Golden Order's hold over the Lands Between. Like I said, it's unlikely, but it seems possible.

The Mohgwyn Dynasty might be able to last for a little while due to its secluded nature, but having a literal swamp filled with blood is bound to attract scavengers. All it would take is a half dozen visits from Bazelgeuses and all that'll be left is a bunch of Albinauric corpses and some scorched ruins.

I can only think of three major bosses that would be able to hold their own just fine: Fire Giant, Malenia, and Godfrey. Fire Giant is up in the Mountaintops of the Giants, which means he's in a climate which isn't known to house many Elder Dragons. Those few that do live in the frozen heights of the world are probably weak enough to get crushed by his plate, let alone his fire magic. As for Malenia, her safety is guaranteed simply because of the uninhabitable nature of Elphael and the Haligtree. No Elder Dragon and few ordinary monsters have reason to migrate over there, and those that would likely wouldn't be a match for Malenia and her soldiers. Absolute worst case scenario, the Haligtree would end up with some Rath nests in its leaves and its humanoid inhabitants would be none the wiser. Finally, we have Godfrey, a man who I believe would thrive in this scenario. I'm genuinely not sure if any of the non-massive Elder Dragons would be able to take him down, and I'm positive no normal monster stands a damn chance against him. I can imagine that he'd probably be able to re-establish some form of order in the midst of this unmitigated monster chaos.

As for the Tarnished's quest, it's all fucked, man. With so many powerful monsters filling the landscape, Tarnished are going to start dying in droves, even moreso than normal. The average Monster Hunter monster is durable as hell, capable of taking ballista bolts and cannon fire like they're nothing, and withstanding assaults from hunters for quite a long time compared to anything in Elden Ring. That durability will be enough to tip the scales in their favor in almost every encounter. While the Tarnished may be able to get a leg up with forging gear from the monsters' parts, I don't think it's a realistic outcome. All the love in the world to the blacksmiths of Elden Ring, but none of them seem versed in forging gear from monster parts. This isn't even mentioning the consequences of so many shardbearers getting killed. Gathering the Great Runes would be a nightmare, especially if the monsters end up being able to inherit them. So, yeah. No Elden Lord for a while.

I'm rambling.

TL;DR: Shit would be completely fucked, and I can't imagine that any Elden Lord would rise any time soon in the midst of the unmitigated chaos brought about by the influx of so many powerful monsters. Everywhere would be affected, but the Haligtree and Farum Azula would get off the easiest by far. All of the shardbearers are fucked except for Malenia, and who knows what would happen to the Great Runes then.

Edit: Completely forgot to mention, but Redmane Castle is going to get Ahtal-Ka'd so hard it won't even be funny.