I found a relatively simple explanation of gravitational waves at: http://www.tapir.caltech.edu/~teviet/Waves/index.html "Relatively simple" because I don't yet understand all of it, and it seems inappropriate for an introductory physics course (although it might work in a junior-senior year course). It does have nice simulations of the basic concepts and makes the analogy between EM waves and GW, as John Denker did. According to the web site, GR is not necessary for GW but special relativity is. Einstein discovered the possibility of GW about a year after publishing his GR theory but thought the waves too small to ever be detected. To have a GW, gravity disturbances must travel at a finite speed (which turns out to be c). But, in Newtonian theory, gravity acts instantaneously everywhere in the universe, so waves are not possible.
The web site does give a simple formula for estimating the strain (h = 2 dL/L, with dL = the change in the length L) caused by a GW as obtained from scaling arguments (as John Denker used for GW power):
h = (GM/c^2)*(1/r)*(v/c)^2
Where: G = universal gravitational constant, M = accelerating mass, c = speed of light, r = observation distance from accelerating mass, v = speed of accelerating mass
Using this formula for the idealized problem Ludwik originally proposed (two suns colliding and assumed to start at rest from infinity with no other complicating factors), I get, at a distance of 1 AU, h ~ 10^-13 (using a final combined closing speed of 6.18 x 10^5 m/s as David Bowman did). By comparison, the recent Advanced LIGO observation of GW from two inward spiraling black holes produced a peak h on earth (1.3 x 10^9 light years away) of ~1 x 10^-21. So the signal from the GW from the two colliding suns at 1 AU is orders of magnitude above the sensitivity of the Advanced LIGO. This I think was the core of Ludwik's question.
As a check, using the same formula for the recent reported Advanced LIGO GW observation of GW from two inward spiraling black holes (M = sum of two black hole masses = 65 solar masses, f = 150 Hz at peak signal, r = 1.3 billion light years = 1.27 x 10^25 m) I get: