To get started, here is the slideshow (with cats) of the words you have seen before:
1. Inops, potentem dum vult imitari, perit.
(A) poor (person), when he wants to-imitate (a) powerful (person), perishes.
inops, po-TEN-tem dum vult imi-TA-ri, perit.
Here is that passive infinitive: imitari, and it is passive in form but active in meaning, so it takes a direct object: imitari potentem, "to imitate a powerful person," where potentem is the accusative form of the adjective potens, being used substantively as a noun. You haven't seen this adjective before, but you have seen a related noun: potentia.
2. Esuriens venter non vult studere libenter.
(A) hungry stomach doesn’t freely want to-study.
e-SU-riens venter non vult stu-DE-re li-BEN-ter.
The word studere, "to study," is the infinitive form of the verb studet, "studies," which is the origin of English "study," "student," etc.
3. Felis amat piscem, sed non vult tangere flumen.
(The) cat loves fish, but doesn’t want to-touch (the) water.
felis amat piscem, sed non vult TAN-gere flumen.
The word tangere, "to touch," is the infinitive form of tangit, "touches," as in English "tangible."
4. Bos ad aquam tractus non vult potare coactus.
(An) ox led to water doesn’t want to-drink, coerced.
bos ad aquam tractus non vult po-TA-re co-AC-tus.
The word potare, "to drink" is the infinitive of the verb potat, "drinks." This is a new word, but you have seen the related noun: potus.
The word aquam is the accusative form of aqua, used with the preposition ad, which takes the accusative case.
5. Error in orbe gravis: vult porca docere Minervam.
(A) great delusion in (the) world: when a-pig wants to-teach Minerva.
error in orbe gravis: vult porca do-CE-re Mi-NER-vam.
The word porca means "pig" as in English "pork." You've actually seen a much reduced form of this saying: Sus Minervam. Now you can see a fuller form, with the verb included: sus (=porca) vult docere Minervam. The word Minervam is in the accusative case, the object of the infinitive docere.
Here's a recap:
- Inops, potentem dum vult imitari, perit.
- Esuriens venter non vult studere libenter.
- Felis amat piscem, sed non vult tangere flumen.
- Bos ad aquam tractus non vult potare coactus.
- Error in orbe gravis: vult porca docere Minervam.
Plus the LOLCats!