Can you help me with that?

X with Y has a lot of meanings. One meaning is "uses Y in doing/achieving/obtaining X".

So you can think of this as meaning "Can you help me to use/do/get that?"

Can you help me on that?

X on Y has a lot of meanings. One meaning is to say Y is a topic, when X is a conversation or other event where information is exchanged, such as a class, book, etc.

So you can think of this as meaning "Can you give me any help regarding the topic of Y?"

Can you help me about that?

X about Y has a few meanings. One meaning is that Y is something to understand or learn. Another meaning is that you are near Y such that you can be considered exposed to it.

However, about kinda-sorta has an underlying "need" to work like a location (and it also has a less common meaning that's related to location as well). Therefore, verbs with about generally tend to be "directed" with to.

When the meaning is similar to on Y above, the concept is that you are being "exposed" to the knowledge.

Help is not a verb that can take a complement that's a location, so help me about X is weird. But there's other verbs that work fine.

I'm walking about the rose garden. (you're physically in the rose garden)

Show me about the roses. (can mean take me through a rose garden or introduce me about your rose collection)

Can you talk to me about that?