I'm especially interested in the difference between the first two. Some people have said prejudice is when a stereotype about a group is applied to an individual, but a lot of places (even within psychology) talk about prejudice as though it can also apply to a group. Allport described prejudice as an "antipathy" towards another group, but that doesn't seem to describe implicit prejudice. How exactly are these terms defined?
The terms are sometimes used a little differently. Nevertheless, in psychological research, there is quite some consensus about their use. For example, reflecting the most prevalent view, the Resolution on Prejudice, Stereotypes, and, Discrimination of the American Psychological Association (2006), defines them in the following way:
prejudices are unfavorable affective reactions to or evaluations of groups and their members, stereotypes are generalized beliefs about groups and their members, interpersonal discrimination is differential treatment by individuals toward some groups and their members relative to other groups and their members, and institutional discrimination involves policies and contexts that create, enact, reify, and maintain inequality (Dovidio, Brigham, Johnson, & Gaertner, 1996; Eagly & Diekman, 2005; Fiske, 1998; Lott & Maluso, 1995; Mio, Barker-Hackett, & Tumambing, 2006; Myers, 2005; Nelson, 2005; Shih, Pittinsky, & Ambady,1999)
In other words, if Person A does not like (has a negative emotional reaction toward) the Lokai in general, or Person B (whether explicitly or implicitly) in particular because this person is a Lokai, that's prejudice.
If Person A believes that being a Lokai makes Person B a treacherous, lazy, and dumb guy, but a great cook and guitar player (you have to grant them that!) that's a stereotype.
If Person A doesn't invite Person B to his/her party because he/she is a Lokai, that's discrimination.
How exactly are these terms defined?
Not exactly. Many terms are not used consistently in science therefore different scholars will use them in different ways. Furthermore, as there is little merit in doing so, few scholars will generally attempt to differentiate complex and contested terms. With this considered there will probably not be a clear objective way to differentiate stereotypes, prejudice and discrimination - you may need to make an argument based on assembling relevant discussions of each individual concept.
This is how I understand it. A stereotype is rule of thumb about how to think about/act toward a specific type of entity. You can have a stereotype about anything - not just about people. Prejudice is generally considered to be a (negative) prejudgment of something/someone. In some sense a prejudice is therefore just a negative stereotype about a person (or group of people). Discrimination is generally considered to involve treating someone less well (in terms of behaviour rather than just attitude) due to some characteristic(s) of theirs. Discrimination is therefore essentially a behavioural manifestion of prejudice.
To give an example, a bouncer associates people of one race with being violent (a stereotype). He is therefore more likely to prevent people of that race from entry to his night club (prejudice). He prevents two member of that race from entry on a specific night (discrimination).
That isn't a perfect example but I hope it makes things a little clearer. Let me know if you want more details or clarification.