Accessibility, Usability and Validation: Are they synonymous of one another?
They are not synonymous [having the same or a similar meaning] else we would not be using three when any one would do. They are, however, compatible [able to exist and perform in harmonious or agreeable combination].
Accessibility: being at hand when needed.
Usability: being fit for use; being convenient to use.
Validation: testing the truth (valid proof) of something.
I visualise the three as a dynamic Venn diagram sliding together or apart depending on site requirements, budget, and time. Given both individual and technical variants I am unable to imagine a total overlap of any two, let alone all three.
* Is a w3c valid site necessarily easy (fit/convenient) to use?
* As noted by pageoneresults some (and there are several models) accessibility guidelines require grammar validation but it remains but one requirement among many. What combination of validations is valid?
* Is a site that is easy to use for me easy for you, or vice versa?
* Is a site that is easy to use necessarily valid?
* Is a site that is 'at hand' necessarily easy to use? or valid?
And then there is the quality of available tools. The major browsers for the not-so-seriously-handicapped-majority are unable/unwilling to render similar results. Imagine the lack of support and capability variance among the various browsers for the more-seriously-handicapped-minority.
These are not reasons to ignore validation, usability, or accessibility. Nor reasons to address only their 'similarities'. They are three very different creatures and if we address only the overlap many people, albeit a small percentage of the whole, will remain ignored.
Can you have an accessible and usable website without HTML and CSS validation?
Depends on your definition of "accessible and usable".
Whose regulations? Whose requirements? Whose suggestions?
For practical purposes (as you noted) grammar validation is often one accessibility requirement. In that instance certainly and in general best practice the answer is no, you can not have an accessible and usable website without HTML and CSS validation.
However: accessible is not automatically usable, nor is usable necessarily accessible. And valid may be either, neither, or both.