Modern academic English grammars now usually recognise prepositions as a class of words which just like nouns, verbs, adjectives and adverbs head their own phrases, have their own distribution and tend to take the same kinds of modifiers and other dependents. In the same way that verbs often take NP Complements which are often referred to as Objects, so do prepositions. However, just like verbs, prepositions can take other types of Complements or may take none at all. These and the following kinds of observations also apply to adpositions in many other languages.
Ever since Jespersen was writing in the early 20th Century, a growing number of grammarians have recognised that the word after is the same type of word in the following types of example:
- I met her after the concert.
- I met her after the concert started
- I met her after.
Here we see after taking an NP complement, taking a clausal complement, and occurring with no complement at all.
The same goes for the following instances of outside
- She was outside.
- She was outside the building.
Even when they take no complement, after and outside still behave like prepositions and not like adverbs. For example, in so-called standard Englishes, prepositions can be modified by the specialised adverb right , which adverbs generally can't be:
- I met her right after (the incident).
- She was right outside (the building).
- *She lives right locally.
They cannot be modified by very, unlike most adverbs:
- *I met her very after (the concert)
- *She was very outside (the building)
- She lived very locally.
Unlike adverbs they can freely occur as complements of the verb be:
- That was after (the incident).
- She was outside (the building).
- *She was locally.
Unlike adverbs, prepositions and preposition phrases freely post-modify nouns:
- the day after (the incident)
- the man outside (the building)
- *the day subsequently
- *the man externally
There's lots more that could be said here.
The Original Posters examples:
- two days before Easter
- two days before
In both of these examples the word before is best analysed as a preposition and the phrase two days as a measure phrase Modifier of that preposition.
Just a quick note on the supposed post-position ago. The preposition ago always occurs with an obligatory measure phrase. Being obligatory, such measure phrases must be considered Complements of this preposition. However, with verbs, for example, not all NPs that occur as Complements are considered Objects. So in She was an acrobat, the NP an acrobat is considered a Predicative Complement, not a Direct Object. With prepositions, the NPs occurring as Objects typically denote some kind of 'anchor' with respect to which some other entity or action is oriented. With intransitive prepositions, this anchor is often omitted because it is recoverable. The anchor is often the present moment or place being talked about. With the preposition ago the anchor is the present time. The fact that ago occurs with an obligatory measure phrase does not mean that that measure phrase has the same kind of function as an NP Object of a preposition or another right-hand side Complement of a preposition. It has the same kind of semantics as, and similar grammatical properties to, a measure-phrase Modifier within preposition phrase structure. As such, although many grammars may analyse it as one, it is not a postposition in the normal sense of the word. This contrasts with other genuine candidates for postpositionhood in English:
- the whole day through
- this point notwithstanding, ...
- this question aside, ...