Every post on Math Stack Exchange (MSE) should be as self-contained as possible. This means that a sufficiently expert reader here should be able to understand your post without needing to view some external resource. This applies to both questions and answers.
As such, you should include the important details in the post. If this means copying definitions, then copy those definitions. If it means quoting a significant portion of the exposition, then quote that exposition. Of course, you should also provide links to the original material.
That being said, if you are copying significant portions of the source material into a question on MSE, then you might reconsider your question. If a reader absolutely must be familiar with every detail of every one of several definitions from some other source, then your question is probably not a very good fit for MSE. What is described in the question sounds like a question which is either
related to active research (in which case, Math Overflow might be a better fit), or
overly broad (narrow it down to one or two definitions and perhaps a theorem, then ask a more focused question).
Expanding a little on the second case: I agree that a long question with a lot of definitions is problematic, but hiding all of the definitions behind a link or reference doesn't fix this problem—indeed, it makes it worse, because readers have to expend more effort to understand your question. Rather, you should think about how to more narrowly focus your question and make it easier for potential answerers and other readers to get to the point. A few ideas:
Put the question right at the top. Set it off from the rest of the text, and ask in as concise a manner as possible. You should be able to reduce your question to a single sentence; maybe a short paragraph in the worse case. This helps the reader with the rest of your post, as they will have a better idea about what to look for as they skim over the remaining context.
Provide a link to the source. An interested reader can follow up if they want, and it is possible that the source will provide some context for a narrow set of users (i.e. those already familiar with that source).
Include only those parts of the original text which are really crucial to understanding the question. This might mean editing some definitions or theorems down to a couple of key statements, and leaving expository material out entirely (unless the question is about the exposition). Again, if you are finding it necessary to copy more than a couple of definitions into a question, then your question is probably too broad, and needs to be more narrowly focused.