When we think of "additional" or "extra" parts of the sentence like this we are thinking about functions not parts of speech or types of phrase.
The proper terms for this type of function is ADJUNCT. An adjunct is part of a sentence that is not necessary for the grammar. This means it is not necessary for the sentence to be grammatical or make sense.
The subject and object are COMPLEMENTS of the verb. Certain verbs set up slots for both subjects and objects; some for just subjects; some for subjects, objects and other complements. If part of a sentence is filling one of these slots, it is a complement of some description.
However, the sections in bold in the Original Poster's question:
- to the finance department
- at the restaurant
- with Mr. Barber
... do not fill any of these slots. They are entirely extraneous in terms of the structure of the sentence. The sentences are perfectly grammatical without them:
- He was giving a presentation.
- She was having lunch.
- They were going to a meeting.
It is this property of not filling a particular slot in a sentence or phrase which makes an adjunct an adjunct.
One last thing to mention is this. Often, when we talk about adjuncts, we are talking about the structure of the sentence in terms of immediate constituents of the verb phrase. However, strictly speaking, adjuncts can occur in any phrase. A good illustration is the Original Poster's third example:
- They were going to a meeting with Mr. Barber.
Now if Mr Barber was going to the meeting with them, we would regard this as an adjunct in the verb phrase - in other words as a general adjunct of the sentence.
However, if they are travelling to the meeting without Mr Barber, but Mr Barber was at the meeting, then with Mr Barber is an adjunct in the noun phrase 'a meeting with Mr Barber'. Here the preposition phrase with Mr Barber is modifying the noun meeting, not the verb phrase were going to a meeting. We therefore say that with Mr Barber is an adjunct in the noun phrase. It is not filling any special slot in the phrase. Notice that this noun phrase, a meeting, is well-formed without the preposition phrase.
One last addendum: some people refer to adjuncts as ADVERBIALS. However, this is a bad term as it has associations with the word adverb. Now adverb is a part of speech, not a function in a sentence. Generally speaking, writers who use the term 'adverbial' are generally unable to distinguish whether they are talking about parts of speech, types of phrase or functions. The terms is confusing and those who use it are - more often than not - unwittingly confused! It is a term that should be banished from any serious discussion of English grammar.