I think it is the use of the term object that is problematic. You suggest the three types of objects that are commonly identified in traditional grammar and also in linguistics, though terms like patient, adjunct argument and complement are more common. But these all identify very different types of syntactic and semantic relations.
(using the notion of complement quite broadly as any modifying word phrase...)
- "Direct Object": is a verb complement (patient) in an object relation: it identifies the thing (object) that receives the action (or state) of the verb
This is the traditional definition of an object, the one we all learn in middle school grammar classes and it makes a semantic distinction, one which is also included in the linguistic definition of the term along with other syntactic distinctions which differ from langauge to language. But as a simple semantic definition, it doesn't hold for the two other types of objects you identify because in linguistics the "object" really has little, if anything, to do with semantics, even when it is used to identify a "direct object". The term object is always going to have some semantic content, even if linguists don't use it that way.
- "Indirect Object": *a verb complement, adjunct or argument: usually indicates the direction or purpose of the action (to/for someone or something, a semantically adverbial relation) in a unique construction that fronts the adverbial (complement) ahead of the verb's object.
According to the semantic definition in 1 above, this isn't an object at all - at best it's an adjunct or argument (syntactic) but its semantic relation is adverbial - it says something about where or why the action happens. This use turns a semantic distinction into a syntactic one. If one is going to use semantic labels to identify verb complements, they'd be more consistent if it was labeled an adverbial relation rather than calling it an object. But that's just me.
- "Prepositional Object: identifies the thing that receives the relation of the preposition with its antecedent (usually a verb or a noun) - usually functions syntacitcaly as a verb complement or a noun complement
If the relation's antecedent is a verb, then it is a verb complement and most often in an adverbial relation to the the verb. If the antecedent is a noun, the prepositional phrase is syntactically a noun complement. Not all linguistic frmaeworks use this term and instead may call it a landmark of the preposition, or something else.
These are all very different semantic and syntactic relations and it would be at least more clear if they did not all share the same term. I'm always amazed at how well linguists juggle these terms and manage to keep their origins in mind, while most of us mortals seem to botch them at every turn. It makes the question of what is an object seem, I dunno, somewhat Quixotic.