Why can't I say like "Is there something I can help?" And what does the particle "with" mean in that case? It is usually at the end of the sentence, is it a transitive verb?
When to help is used without a preposition between the verb and the object, as in Fertilizer helps plants to grow) the object (plants, in that example) is normally the person or thing receiving help.
If the object represents the problem (that someone needs help solving), the standard preposition usage is I can help [you] with this problem (where you/this problem are the direct/indirect objects).
There are a few contexts where this distinction isn't always quite clear. For example...
...where in both cases we could include with, but it's not required. I think in all such "borderline" cases, the "object" (digestion, sleeping) represents something with a "normal, unproblematic" state (the prepositionless usages above "personify" the action, and help it to "achieve" that state).
Sometimes (lemon oil ... helps heartburn), the "unproblematic state" is when the "object" doesn't exist.
The net consequence of the above is that OP can validly ask Is there someone I can help?, but if asking about a thing (a problem that needs to be solved) the preposition is required.
You could understand with in such constructions as meaning within the context of [the problem].
You usually help somebody, not something. And you can help somebody with something. By asking this question you essentially are saying "I can help you with anything". The person whom you address then can think of something from all with which they are currently occupied in conjunction with your statement and suggest the activity you both can jointly undertake.
Think of it this way...
An answer to this sentence is
Yes, I need help with my homework.
No, I don't need help with anything.
In these cases, you can see that there exists something that the helper could have helped with ('homework' and 'anything'). This is what the "with" in your question is linking to. If you wanted to make a sentence without "with", you could say something like "Is there any way I can help you?".