Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very successful and many other theories. But gravity and electromagnetism are long range in nature and classical as well. Can these two be unified independent of weak and strong forces?
Yes, classically, we can unify gravity with electromagnetism. The theories that do so are the famous Kaluza-Klein theories. They are theories of pure gravity in $4+1$ dimensions rather than our usual $3+1$ dimensions. When such theories are viewed from a $3+1$ dimensional perspective, the effects of gravity in the fourth unseen dimension appear in the lowered $3+1$ universe as electromagnetism! This is really amazing (the Professor who taught me GR titled the topic on the Kaluza-Klein theory as The Kaluza-Klein Miracle in his notes!). Now, the lesson physicists learned from the KK miracle is that what makes this miracle possible is the fact that pure gravity in additional dimensions appears as gauge-fields in lower dimensional universes. The more evolved version of the spirit of the KK miracle is survived in string theoretic theories which naturally (and inevitably) unite electromagnetism (and all other forces) with gravity--in addition, these theories are inherently quantum mechanical too.
Now, of course, we don't yet have explicit experimental evidence for any of the string theoretic theories (we also don't know which string theoretic theory reproduces the standard model). But yes, theoretically, we can construct consistent theories that unite electromagnetism with gravity.
Of course, KK theories are not a part of the "done-deal" physics, among various reasons that I am not well-educated in, the major reason is that we don't have experimental evidence for the extra dimensions. Nonetheless, KK theories are a part of textbook physics and for very good reasons. They do provide an internally consistent classical framework to unite electromagnetism and gravity and teach us how pure gravity in a higher dimension can give rise to gauge-fields in lower dimensions as I already mentioned. And this insight is now a part of the daily toolkit for theoretical physicists.
Most physicists are not interested in unifying just gravity and electromagnetism, because electromagnetism is already fully unified with the weak nuclear force. They’re now sometimes just called the electroweak force.
Furthermore, the strong nuclear force has closer similarities to the electroweak force than gravity does, and Grand Unification of the strong and electroweak forces may be an easier next step.
Most physicists also have no interest in classical unification, when quantum physics is a more successful explanation of reality than classical physics. Classical electromagnetism isn’t even a correct theory, so why would we want to unify it with anything?
There is no acceptable field theory of gravity, which should describe gravity as a field defined on Minkowski space like electromagnetism, and there is no acceptable theory that describes electromagnetism as a curvature of space . It will take one or the other to make a unified theory at all possible.