Quick video from the Japanese ryona board for those waiting. This doesn't contain all of the grabs or characters. Looks like the uploader only chose those that interested him. Anyways there are also certain enemies and bosses with grabs that wander each stage.
Berserker - A large black mutant creature. These guys will rush at your character and pin them to the ground. If you don't press buttons fast enough it will bite down on your characters head and swing them around for a second or two. It will then grab your character with both of its hands and pull with its mouth, as if trying to tear their head off. Unfortunately your character dies and falls to the ground after a second of tugging. No decapitation or anything like that. It might be different for foreign copies but I wouldn't hold my breath. Still, I like how the character kicks their legs when their head is in its mouth.
Mutant Plant - Giant plant sprouting from a single, thick, curled stalk. The plant will grab your character with its mouth if they get too close. It will then swing them around before biting(?) down on them, killing them. Like the Berserker the corpse just falls onto the ground. No swallowing or gore.
Kraken - The Kraken is, as one would guess, a gigantic squid. During your fight with it it can lift its body to expose its mouth. The mouth can telescope out to grab your character, at which point it will start chewing on them, draining their health. Again just like the Berserker and Mutant Plant your corpse will simply fall on the floor if you die in the grab.
Parasite - These are large slug/worm-like creatures that usually appear wherever the Kraken does. They can leap onto your character and swallow them whole. If you're inside one your health will slowly drain. Unfortunately much like the other enemies in this list if your health drains all the way the Parasite will simply pop, freeing your character who will then fall to the floor dead.
Characters can also be electrocuted, frozen solid, and gassed.
Most of the creatures mentioned above can appear in the multiplayer maps. But you often have AI or other players to contend with. Typically you're limited to your choice of character in the campaign but if you beat the entire thing you can choose any stage you want and play through them with any character. Makes things a lot easier when looking for ryona. There is also a simulator/training mode that lets you choose characters so you can test out grabs on female characters. That simulator mode is shown in the video I posted.