What is the general term that describes subjects and objects? (direct, indirect and prepositional objects)
John gave Jack money with enthusiasm.
John is the subject, Jack the indirect object, money the direct object, and enthusiasm a prepositional object.
Is there a general term that describes the "things" involved in an action/verb?
Nouns doesn't work because there are pronouns. "Nouns and pronouns" doesn't work because there are gerunds that can also be objects, for example He likes swimming.
I have been using "things" to describe them, but it sounds lame :/
I think the term sought after is arguments of the verb. This term doesn't only refer to the different elements in action verb constructions, but in any clausal construction. In the Original Poster's example John, Jack and money are the three arguments of the verb GIVE. Enthusiasm is not one of the arguments of the verb. There is no special grammatical relationship between give and with enthusiasm. Rather with enthusiasm is just giving extra information in the sentence. It is, therefore, an adjunct in the clause structure.
Some verbs, like the verb HAPPEN, usually only have one argument:
- Accidents(1) happen.
A verb like BET usually has four:
- Bob(1) bet the dragon(2) fifty euros(3) that he would win the contest(4).
The arguments here are, Bob (subject), the dragon (indirect object), fifty euros (direct object) and lastly the content clause: that he would win the contest (complement). The content clause there is a complement of bet, but I don't think that the function it is carrying out has a special name - unlike for example subject.
Verbs, clauses, adjectives and so forth can all be arguments of the verb. So in, for example:
- To swim can help such conditions.
to swim is an argument, the subject, even though it is a verb.
Each argument of a verb in an utterance will have a grammatical function and a thematic role. In:
- Bob was beaten by the dragon.
Bob is the subject. It has the thematic role of patient; in other words it describes the recipient of the beating action. In:
- The dragon beat Bob.
Bob is the direct object of the verb, but still has the thematic role of patient.
In short, the number of arguments that a clause has depends on the number of slots set up to be filled by the verb. These arguments may have different grammatical functions and different thematic roles. Arguments can also be of many different types of word or phrase.
Different linguistic frameworks call them different things. The two most common are, I think, constituents and arguments.
Note that in your example only John, Jack and money are arguments. from his wallet is a relative clause which modifies money, and it doesn't have any kind of similar role as the arguments.
Some writers use the word function.
Function - In linguistics, the relation between linguistic units in a hierarchy: the adjective large functions as a modifier of the noun house in the noun phrase that large house, and in turn that large house functions as subject in the sentence That large house belongs to Jill’s parents. (Tom McArthur (ed), 1992.423, The Oxford Companion to the English Language )
In some analyses of syntax these consitutents of a clause (or of subordinate constituents) are called NPs, a term which derives from “noun phrase” but has a somewhat larger scope: a “noun phrase” is a phrase headed by a noun, while “NP” includes phrases of other sorts which can act in the same syntactic role as noun phrases.
Note that an NP (or “noun phrase”) can be a single word—John, Jack and money are all NPs—or it may include a noun and its dependents, such as a determiner and modifiers, as in his wallet, which is the object of the preposition from.
A verb’s subject and objects are collectively referred to as its arguments.