There are no gravitational waves in the Newtonian gravity.
A wave is defined by its shape: it is something that depends on space like $\cos(kx)$ but nothing like that can be produced by Newton's gravity whose action is instantaneous. In the standard Ansatz for a wave,
$$\exp(-i\omega t +i k x),$$
one has $k=\omega/c$ but if $c$ is sent to infinity, $k$ goes to zero and the space dependence disappears. So you can't really be talking about waves - something that has a periodic dependence on the spatial coordinates. There aren't any.
Also, for equivalent reasons, according to non-relativistic mechanics, an orbiting binary star isn't losing any energy by the emission of gravitational waves because there aren't any. If there are extra objects in space besides the binary star, they will influence the internal motion of the binary star (a three-body problem) but this is in no way equivalent to the effect of gravitational waves. In particular, there's no "guaranteed sign" that would ensure that the internal energy of the binary stars decreases. It would go up and down equally often. The energy is only carried by the "point masses" and not by "gravitational waves" because there aren't any.
In non-relativistic mechanics, you may only talk about time-dependent gravitational fields. But it's only the quadrupole moment that may be periodically changing if the source of gravity is changing. And the gravitational force from an oscillating quadrupole goes like
$$ \cos(\omega t)/r^4.$$
I added two powers of $1/r$ to the Newton's $1/r^2$ inverse square law. On the other hand, if there are gravity waves, they - e.g. the magnitude of $\delta g_{\mu\nu}(x,y,z,t)$ - depend on the location as
$$\cos(\omega t-kr) / r$$
because the density of energy goes like the square of the amplitude above and $1/r^2$ is the right way how energy spreads in space (gets distributed over the spherical area of $4\pi r^2$). Note that the multiplicative difference between the true gravitational waves in general relativity - that go like $1/r$ - and the time-dependent quadrupole in Newtonian gravity - that goes like $1/r^4$ - is $1/r^3$. That's a huge difference, especially if the distances are very large.
Consequently, the effect of the quadrupole decreases much more quickly with the distance from the source than the intensity of the gravitational waves. Obviously, one can't measure the former if we can't even measure latter - the latter, gravitational waves, is incomparably larger than its Newtonian artifact, but we still haven't managed to measure it.
So the whole idea that there is something like "gravitational waves" in non-relativistic gravity is totally misguided. This comment is not meant to say that one can't measure time dependence of gravitational fields. Of course that one can. Ocean tides that change twice a day are exactly an example of a periodic change of the higher moments from other celestial bodies - the Moon and the Sun.
But they're not "waves" in any sense because the energy isn't carried away by those would-be waves, and it isn't distributed over the sphere as the energy of waves would. It's up to you whether you consider ocean tides to be an example of "measured gravity oscillations of nearby rotating masses" - I think that you should. But this observation only means a tautologically trivial thing - that changing configurations of matter produce changing gravitational forces - and this trivial thing is in no way analogous to gravitational waves which are independent objects that exist according to general relativity.
