I suggest trying to break things down into simple English.
Agile - able to move quickly and easily.
Methodology - a system of methods used in a particular area of study or activity.
Model - a thing used as an example to follow or imitate.
Process - a series of actions or steps taken in order to achieve a particular end.
If I was to sum it up (and no one is saying I am right):
The Agile Methodology is what is described by the Agile Manifesto.
The Agile Process is a process that tries to accomplish this, whatever the end. So, Scrum does this generically (but is popularly used for software development - it was also used to manage construction of Heathrow Terminal 5 in London, UK). XP does this just for software development (or programming), and so on so forth.
An Agile Model would be the implementation of an Agile Process done at a company that another company is trying to copy or replicate. This might have more details and specifics in it, INCLUDING the Agile Process that was followed, how many staff were on what teams playing what roles, etc. etc.