There is definitely a usage and etymological dimension to this issue, which I can elaborate on, if you'd like. (It's an issue I come across frequently, and is particularly relevant in regards to original work.)
The use of "Agent" may have arisen partly out of Game Theory, with ideas like "multi-agent systems", possibly because it's quite general (i.e. one does not have to say participant, or player, or actor, etc., and it is species non-specific.)
"Automata" seems to be favored in some circles, and although this term was originally reserved for physical, mechanical devices, it now encompasses a range of physical and information-based systems (with perhaps a contemporary emphasis on the virtual. A famous extension is the categorization of Conway's Game of Life as a "cellular automata". Conversely, "robot" would seem to have usurped "automaton" for physical systems.)
I tend to use agent when I'm thinking in an economic sense, or in a game theory sense as related to computing, and automata when thinking in a procedural sense in terms of algorithmic intelligence. But the distinction is partly semantic.
Robot seems to be avoided in the academic literature in regards to information systems, possibly because of the deeply entrenched popular understanding of "robot" as physical automata. The use of the informal "bots" for describe information-based systems seems to have arisen in the public sphere. I like the term bots as it is being currently applied, but I feel it has the connotation of trivial systems, and haven't really seen it used for for strong AI.