It really depends on the country of origin (and thus the system of law they're operating under).
In the United States, there aren't many solicitors left. A few exist in official federal capacity (such as the Solicitor General, who appears as the advocate of the U.S. Government in Supreme Court cases), but for the most part they are nonexistent. This is especially confusing when you factor in that the most common use of the AmE 'solicitor' is as another name for a door-to-door salesman (hence the "No Soliciting" signs you see on some doors). As for the other two terms, the U.S. 'attorney' is simply the proper title of a practicing lawyer; they are in most cases synonyms (unless the lawyer isn't allowed to practice law for some reason, like being disbarred).
In the United Kingdom, there is no such thing as an attorney. Lawyers are divided into solicitor and barister classes; solicitors are the lawyers who sorta "run the system", while baristers are the personal advocates for conflicting parties.
Other countries that have combined the roles of barister and solicitor include Canada, New Zealand, the US (obviously, as I just detailed that), and most of Australia. And the South African law system uses 'attorney' in place of 'solicitor' (the South African attorneys and advocates fulfill similar roles as the British solicitors and baristers, respectively).
I could go into far greater detail, but I think that's missing the point of your question. So I'll answer it in fewer words:
Depending on the country, some of those terms don't exist, and some others are conflated. Without knowing which law system you want to know more about, I cannot adequately answer this question. However, if I were to assume that you were most interested in the American legal system (the one I have most familiarity with), then attorney=lawyer, and solicitors basically don't exist in a legal capacity.
I hope that helps!