There are actually two different questions here:
1) Does the concept of a Fermi-liquid extend to non translationally invariant systems?
2) If I have some kind of "slowly varying" perturbation to my electronic system, it should still look locally like a translationally invariant Fermi-liquid and hence have a well defined Fermi-surface locally. How do I extract the local parameters of my local Fermi-surface, locally speaking?
The answer to question one is yes, the Fermi-liquid concept extends. In the sense that the low energy theory is still a theory of weakly interacting particle-hole pairs and Cooper pairs. In the presence of disorder there is, as you say, no conserved momentum, but this means only that the pairs obey a diffusion equation instead of a wave equation. In another sense if I turn disorder on in 3-d Fermi-liquid there is no phase transition until I reach a critical disorder.
Question 2 is a more technical thing. In a Fermi-liquid things oscillate at the Fermi-wavelength, like Friedel osciallations, and the existence of these oscillations is a signature of the Fermi-surface. If we put a smooth external perturbation on our Fermi-liquid we expect things to oscillate at the "Fermi wavelength" where the Fermi wavelength itself is slowly changing with position. Whenever we have a wave with slowlying varying frequency we should Wigner transform. So define a Green's function $G(x,x',\omega)$ where I put an electron in at position $x$ and take it out at $x'$. Define the new function:
$$H(k,\omega;R) = \int dr \exp(ik\cdot r)G (R+r/2,R-r/2,\omega)$$
The function $H(k,\omega;R)$ is roughly what "$G(k,\omega)$ looks like near $R$". If everything is translationally invariant then $H$ reduces to the regular Green's function. The "local Fermi surface at $R$" can be extracted from the structure of $H(k,\omega;R)$ as in $G$ (although the discontinuity will only be approximate). You can write down equations of motion/ Dyson equation for $H$ just like you can for $G$ as long as you keep in mind that the with respect $R$ are much slower than the fermi wavelength.