Isaac Asimov wrote a great essay related to this, The Relativity of Wrong. This quote summarizes his point:
My answer to him was, "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together."
You somewhat touched on this by mentioning Newtonian physics being technically wrong, but still practically useful. This is a key point. Science isn't very concerned with how things actually are. Rather it is concerned with predicting how things will behave under certain specific circumstances. Thinking the Earth is flat is wrong, but operating with a model that the Earth is flat is pretty valid for most of what we do. A more accurate, yet more complex, model is the Earth as a sphere. This becomes the better choice when covering long distances. At the end of the day though, it doesn't matter much that both of these models are "wrong", as long as they continue to provide useful data.
As for the theories you mentioned, the key is that there was never much empirical evidence supporting them. Had there been, then that alone would have made them useful, despite being wrong. Science is not smart people thinking about things and coming up with ideas for how things might be. Rather it is smart people examining data and coming up with models that explain this data and make other testable predictions.
Reading over that wiki list shows a lot of interesting ideas and not a lot of useful models. Relativity is an example of a theory that raises a lot of eyebrows, but has a ton of evidence supporting it. Even if in a generation we discover some serious flaws in relativity it will not fall completely out of favor the way the theories on that list have. The key difference once again, is that relativity agrees with and explains a huge body of evidence. Those "theories" had no real evidence backing them, and often times were simply the first idea people came up with when they had no way to really make detailed observations.
String theory is a good example of an exception that proves the rule. It is a modern theory that may well end up on that list (or its successor). The key is that there isn't much (if any) evidence. It doesn't make any testable predictions yet. String theory may yet turn out to be useful, or it may turn out to be completely bogus. The important difference is that string theory, while widely known, is not widely accepted, and has not provided any useful models.
So, the answer to Are our current theories wrong (in the strictest sense that Newtonian physics is wrong)? is yes. No scientist will argue that we have totally accurate models. But they are useful models, that produce actual results, and are more accurate than any other model previously developed. If that's wrong, I don't want to be right.
