Seismic noise interferometry is an exciting technique for studying volcanoes, providing a continuous measurement of seismic velocity changes (dv/v), which are sensitive to magmatic processes that affect the surrounding crust. However, understanding the exact mechanisms causing changes in dv/v is often difficult. We present dv/v measurements over 10 years in central Iceland, measured using single-station cross-component correlation functions from 51 instruments across a range of frequency bands. We observe a linear correlation between changes in dv/v and volumetric strain at stations in regions of both compression and dilatation associated with the 2014 Bárðarbunga-Holuhraun dike intrusion. Furthermore, a clear seasonal cycle in dv/v is modeled as resulting from elastic and poroelastic responses to changing snow thickness, atmospheric pressure, and groundwater level. This study comprehensively explains variations in dv/v arising from diverse crustal stresses and highlights the importance of deformation modeling when interpreting dv/v, with implications for volcano and environmental monitoring worldwide.