In most situations it would mean that you don't owe me anything in return. Here it would mean there would be no expectation romantically or otherwise. But unless you were socially retarded you would want to be more specific to avoid a misunderstanding. 'Let's go together as friends' would be clear in meaning and intent.

Its a shortened version of "no strings attached". Its common that people will shorten it to "no strings" when its said in normal conversation.

"No strings attached", means there is a benefit without having to return a favor. Say someone asked you "I want to help you do your chores with no strings attached". It means they want to help you without asking for anything in return. "Lets get together, no strings", is different. This is a phrase I, or at least as I an English speaker, would not use. It seems to be open to different meanings but nevertheless; it is ambiguous(not clear to the meaning). If I were you, I would ask whomever you are writing to, to rewrite the phrase or to provide an explanation. My opinion is that you might be getting friend zoned.

"No strings" equals "Without obligations"

Basically, "no conditions".