The more I thought about this, the more I want to answer...
This is a proposal for the rules of your world
Because in the Real World, creatures of dimensions X<3<Y don't exist. Well, maybe they do, but here's the problem: there has never been any evidence of any effect in the Real World that can only be explained by the presence of such creatures (or even passive objects).1
But that's no fun at all!
Can an N=1 creature hurt anything?
No — but it could be yes!
The most complex N=1 creature is a straight line. A very rigid worm, you might say, but because it has no other dimension it's infinitely thin in every direction other than the direction of the line. Being infinitely thin, it has no mass. Therefore, it passes cleanly through any dimension N>1 without damage. At worst, more massive objects deflect it or they just move imperceptibly out of the way to allow it to pass. No molecular cohesion is ever lost.
Unless you want it to. That's the fun of creating rules for your world. If you want N=1 creatures to cause damage, then we need to ask ourselves, "what would molecular disruption look like if a 1D object passed through something?" Let's stay away from atomic cohesion. Disrupting atomic cohesion is called fission and it's nasty. But molecular cohesion... A sheet of metal might be very cleanly cut by such a creature. A living being, where cells have the ability to re-establish cohesion, might not be damaged at all.
Can an N=2 creature hurt anything?
No — but it could be yes!
But remember the N=1 problem. When you look at a 2D creature edge-on, what you're seeing is the 1D edge of the 2D object. It's infinitely thin. We can model that process by hanging a 3 meter x 3 meter sheet of aluminum foil. When you face it, it's opaque. But when you look at the edge (on a very calm day with a very flat sheet), you can't see it. If you walked directly into the edge (and perfectly...), you'd have the same damage properties of a 1D object... kinda.
What happens when that infinitely thin sheet has entirely separated you into two halves? That's a good question! It's infinitely thin, but does that mean it's not there? If the material is impermeable, meaning nothing can pass through it, then you just cut our poor test subject in half. Maybe.
The problem is that "impermeable" is an interesting word. Maybe fluid can't pass through it, but can magnetism? How about the atomic forces? In other words, our test subject may continue walking, and they'd better hurry before the lack of blood, which has stopped flowing, leads to their death. Could the electrical charges in the brain continue to flow in such a condition? The electrons can't pierce the sheet — but would the charge couple to the other side of the synapse?
Ah, the joy of creating rules for your imaginary world!
Even if we consider the other direction, the sheet-on direction, where the 2D object can be very clearly seen by the 3D person because it's blocking sunlight (in your world, an infinitely thin object can be opaque!), but would it hurt to run into it? A 2D object still has no mass because it's infinitely thin. It would cause less notice than running through air! But it's impermeable! So you suffocate because this opaque, weightless object you just ran into is... wait. You didn't suffocate, because the sheet can't be bent. That would require a third dimension. Which means when you hit it, it bounced harmlessly away and you only noticed it visually because you didn't feel a thing.
But how does gravity affect a 2D object? From our Real World perspective, it has no mass, and so isn't subject to gravity. Once tossed in the direction of the sky it would keep on going forever until the face of the sheet struck something else. Hopefully something soft so it stopped rather than bouncing off and continuing its journey. But as we discussed, it could cause harm. If anchored, it would stop a runner. If used to slice into a 3D object and held there, that object would eventually die due to necessary 3D things not having the ability to happen any more — so long as your rules allowed an infinitely thin object to be, for example, impermeable.
To quote Captain Jack Sparrow (second time in two days, imagine that...), "Ah-ha! So, we've established my proposal as sound in principle. Now, we're just haggling over price."
If you're asking about Real Life, the answer is simply "No." If asking about your imaginary world, the answer is, "absolutely yes!" We just need to set the rules.
This Stack often focuses too much on the Real World. There's a lot of cool stuff in the Real World! It's also boring, which is why we read novels, go to movies, and play video games. What makes those flights of fantasy fun is that they invoke rules that aren't identical to the rules here. They let us play the "What If?" game.
I like your world! Cool things happen there! It'd be a scary place because things I can't see can hurt me!
The question is, how do you want them to hurt people?
If my answer has provided you with sufficient inspiration to answer that question, then have at it and consider posting your final story on the Worldbuilding blog, Universe Factory. Some amazing fiction has been written there!
If you're still in need of inspiration and guidance, you'll need to ask a new question. Remember, you need to be specific and you need to describe a problem to solve. Help us understand what you're trying to do and why you're trying to do it. Then explain what's stopping you from solving the problem. We're really good at taking it from there.
1 This is a generalization. There are plenty of people who may jump on this and start talking about Quantum Strings and such things. But that's just arguing for the sake of arguing. No one has ever been garrotted by a quantum string. A lot of physicists would probably be happy if it had happened just once, though.