In this thesis, I present a unified spin-weighted formalism for analysing perturbations to the timing and astrometric observations of astrophysical point sources caused by gravitational waves. The formalism utilises a complex spin field on the sphere and spin-weighted spherical harmonics to analyse ``astrochronometric" observables (combining astrometry and pulsar timing into a single formalism). This approach simplifies the interpretation and simulation of anisotropies in the observables and the derivation of angular cross-spectra and their relationship with generalised Hellings-Downs correlation functions. Additionally, this formalism allows for an explicit connection between correlation components and the spin of gravitational wave polarisations and any chirality present. Furthermore, I evaluate the expected signal-to-noise ratios for these observables to determine their relative utility.
In addition, I investigate the impact of the inhomogeneous distribution of stellar masses on the observed Time-of-Arrival (ToA) of the pulses from millisecond pulsars which travel to us on geodesics that are affected by the space-time metric. The exact path--geometry and red shifting along the geodesics determine the ToA. The metric is determined by the distribution of dark matter, gas, and stars in the galaxy and, in the final stages of travel, by the distribution of solar system bodies. I employ a simple model for the stellar distribution in our galaxy to estimate the scale of static and dynamic sources of what we term generically "geodesic noise". I find that geodesic noise has a standard deviation in order of 10ns for typical lines-of-sight. This suggests geodesic noise is relevant for estimates of Pulsar Timing Array (PTA) sensitivity and may limit future efforts to detect gravitational waves by PTAs.