All this data is potentially out of date, and should be taken with a truckload of salt
Event Agents are mysterious. They can be found anywhere at anytime. There is no known complete database of them but they have been spotted at Planets, Moons, Asteroid Belts, Jump Gates, inside and outside Stations, inside DED Deadspace Complexes and at Celestial Beacons. Some can only be located by scanning while others only appear to players during certain missions.
Most Event Agents offer missions that can only be completed once by players that have the required standings. Event Agents don't give Loyalty Points but most of them will give the player both Corporation and Faction Standing increase as well as some interesting and unique rewards.
However, there are some Event Agents that offer repeatable missions which will give a Faction Standing increase the first time completed and then only Corporation Standing increase each time after that. There's also a few of these Event Agents with a repeatable mission that will only give Corporation Standing increase and no Faction Standing increase whatsoever.
As was stated before, Event Agents are mysterious.
Many online Agent-Finder services have a listing for most of the Event Agents. At last count there were over 700 different Event Agents currently employed by the various Factions in the Eve Universe, including the Rat (NPC Pirate) Factions. Over the years, some of these Event Agents have been classified into groups for ease of recognition by players.
Tutorial Agents (Currently not active)
These Agents offer a one time 2-part mission with Corporation and Faction Standing increase.
These Agents offer a one time 10-part mission with Corporation and Faction Standing increase.
These Agents offer a repeatable mission with Corporation and one time Faction Standing increase.
These Agents offer a one time mission with Corporation and Faction Standing increase.
Most of these Agents offer a one time 2 or more parts mission with Corporation and Faction (Repeatable missions excluded) Standing increase.
These Agents offer a series of missions (Repeatable once every 3 months) with Corporation and Faction Standing increase.
There are still a lot of Event Agents that haven't been classified into groups. In the future, players will surely add more Event Agents into the current groups as well as create more group classifications. Who knows, maybe something like Special Agents?