下種／下衆／下司 are all pronounced "gesu." According to various dictionaries "gesu" can be used to describe a sleazebag, a humble person, or a petty official.
How can one differentiate between which to use? How are they supposed to be used?
Bear in mind that this is an answer based on research and not actual familiarity with the term.
The gist of it is that げす is a dirty word that is generally written in hiragana and refers to things that are socially low, base, vulgar, of the common class. In common use it'll just refer to something crude or vulgar.
Our first stop is an actual J-J dictionary (and not edict which has the unclear definitions you got). See the entry:
Definition one describes a crude or vulgar thing or person. That's where you're getting "sleazebag." The example it gives is げすな考え, or what we can probably call "dirty thoughts" or "having one's mind in the gutter."
The second definition is someone of a low social rank. This is where you'll get your "humble person" definition. The example sentences are slightly archaic so you probably don't need to worry about this one. (For reference: 「―下郎」「女も男もいと―にはあらざりけれど/大和 148」)
The third definition is just a servant, and its examples are also archaic, so don't sweat this one unless you really want to get into your old literature. (「食(めし)たかせける女のむめといふ―なり/浮世草子・五人女 4」)
The 4th is just a low ranking official, or your "petty official." Again, don't worry about this one.
Interesting at the end here is a big list of set phrases that use げす, one of which appears in the alc examples.
Note also that all three of the kanji variations you listed point here and all are indicated as uncommon. Essentially they seem to mean the same thing but you won't normally be using them anyway so the distinction in use becomes more of a historical question than one of choosing the right one for the situation (which I'm assuming to be out of the scope of this question).
So as for how it's used, we check alc:
So we have it on its own just being a classic King Richard. The term げすの勘ぐり is a set phrase that refers to having vulgar thoughts. And then if you want to make a presumption about someone's phallic proclivities, you can go ahead and call them a ゲス野郎. Note that the Japanese doesn't actually refer to any fellatio.
And as a final note, for the kanji just don't worry about it. If you want to use it then pick one and go wild. The word is yours for the bandying so make it count.