You have a good point: depending on the book you are reading, different terms have the same connotation and the same concept may be named differently. In its classic Modern Structured Analysis (not so modern nowadays), Yourdon seems to define methodology in the same way modern authors define process:
More and more large and small organizations are adopting a single, uniform
project life cycle—sometimes known as a project plan or systems development
methodology or, simply, "the way we do things around here."
So, if you are an old school guy like myself, the words "process", "software development life cycle" (or "SDLC") and "development methodology" will all be referring to the same concept: a theoretical framework that dictates what are the phases or activities you should execute in order to deliver your software. Interesting enough, here "methodology" is used caressly because, strictly speaking, methodology means the study of methods, not a particular method. As a matter of fact, the Merriam-Webster on line dictionary states that methodology is the analysis of the principles or procedures of inquiry in a particular field. However, this etymological missuse of "methodology" is now widespread and doesn't matter anymore.
Now, the must. Judging by the Pressman's excellent book (Software Engineering, A Practicioner Approach), that's the meaning of the words process, method and tool:
Process - a collection of activities, actions, and tasks that are performed when some work product is to be created. A process forms the basis for management control of software projects and establishes the context in which technical methods are applied
Methods - provide the technical how-to's for building software. Methods encompass a broad array of tasks that include communication, requirements analysis, design modeling, program construction, testing, and support.
Tools - provide automated or semi-automated support for the process and the methods. When tools are integrated so that information created by one tool can be used by another, a system for the support of software development, called computer-aided software engineering, is established.
As previously noted, "process" is a synonym for "methodology". The latter, in turn, is not meant to be confused with "method" (as it is implied in your question): "methods" are the technical resources you resort to in order to tackle the phases prescribed in your process.
So, the same method may be used in different processes (e.g., E/R modeling can be used by both RUP and XP practitioners). Note that the nomenclature is not neat: it is really weird to state that different "methodologies" can employ the same "methods". No wonder the term "process" is now widespread.
The definition of "tools" given by Pressman in this context is not clear. In a few words, "tools" are the hacks you employ to leverage your productivity as a developer. In order to (try to) clarify all those concepts, think like this: "RUP is a (reference) process to develop a system, E/R modeling is a method to design databases and ERWin is a CASE tool to perform E/R modeling".
All in all, if Pressman is your guy on Software Engineering, you should not employ the expression "software engineering methods" as a synonym for "methodology".
As for the difference between "process model" and "process", Ian Sommerville is pretty clear on that:
a software process model is a simplified representation of a software process. Each process model represents a process from a particular perspective, and thus provides only partial information about that process. For example, a process activity model shows the activities and their sequence but may not show the roles of the people involved in these activities.
So, a "software process model" is a development paradigm, a kind of a very general reference model that inspires the actual software process of your organizaton. In fact, regarding the "software process", Sommerville states that:
The systematic approach that is used in software engineering is sometimes called a software process. A software process is a sequence of activities that leads to the production of a software product.