Your first example is grammatical, the second and the third aren't.
"I would take the dogs out for a walk means that you may perform this action in a future moment if the opportunity arises, if you have the time to do it, and so on.
"I would have taken the dogs out for a walk indicates an action which did not take place in the past (for reasons which are not explained).
"I would took the dogs out for a walk is not a possibility in English, as you cannot use a simple past after "would".
In a different context, another possible meaning for the first sentence is something that you did frequently in the past, an action which you happened to perform and which was discontinued later on. Perhaps this is what you meant by your third definition.