An object is the phrase on which a transitive verb expresses some kind of action. It can be both NPs and subclauses.
I eat candy
I see her
I like chess
I know that she isn't very into science fiction
(there's also the notion of indirect object, such as "I gave her five STDs in one night", "ship me a load of those fudge boxes", "all they told her were lies." (Notice, that one breaks down as "all ... were lies[=COMPLEMENT]", where all [that]=DIRECT OBJECT they=SUBJECT told her[=INDIRECT OBJECT]
A complement is an NP, PP, adverbial phrase or adjective phrase that informs us about the subject:
I am that great!
I painted the house red (notice: the house is the object there)
She isn't at home
She turned frigid once we had gotten our clothes off.
An adverbial is an adverb, a PP or particle or somesuch that clarifies something about the verb. She did not do it, I saw her last night, I swam around in the bay, I long intensely for winter, .. notice, however, that adverbs can be complements as well: I am out of money, I turned the shirt inside out, ...
Some objects in English are prepositional phrases - this is the case with phrasal verbs such as "long for", "wait for", "run up", "stand up", "blow out", "rein in", "take on", etc. Sometimes there's both the option of using a verb with or without an adposition marking its object. In those cases, the phrasal verbs tend to differ in telicity or aspect or somesuch from the non-phrasal one.
"OSV is excellent with rice", with rice isn't even an argument of the verb phrase - it's an adverbial attribute of 'excellent'.
E.g. "excellent with rice" forms one constituent.
People here just do OVS as though it meant [ANY NON-SUBJECT] VERB SUBJECT.
Re: to be, most European languages don't treat it as transitive, but there are languages elsewhere that do parse the complement as an object. This can be tested by object coordination, passivization or whatever other language-specific traits objects have.