What kind of geological (volcanological?) information can be learned from tilt data? Can it also offer predictive benefits, trigger evacuation warnings?
Tiltmeters placed on the flanks of an active volcano can measure changes in the slope angle of the flank. These changes are often inferred to be related to changes in the shape and activity of the magma chamber.
This article provides a quick and dirty example of how these instruments can be used, as well as their limitations.
In this case, the tiltmeters were able to capture the deflation of an erupting magma chamber, but not the precursory inflation. This leads to some inferences about the nature of the magma's ascent through the subsurface.
The article also references studies that were able to detect magma chamber inflation as well.
These kinds of observations definitely add to the body of evidence volcanologists use to assess risk of an eruption, but it's far from a slam dunk.
Here are some examples from that paper, both the long-term trend, and a higher time resolution display during a small eruption:
Fig. 2. Tiltmeter data from V-net (KRMV, KRHV) and Hi-net (MKNH, SUKH) stations during the period from January 23 to February 2, 2011. From here.
Fig. 10. Enlarged view of tiltmeter data during the period from 0:00 to 21:00 on January 26, 2011. Vertical line shows the occurrence time of the small eruption at 7:31 and the beginning of the sub-Plinian eruption, when the amplitude of the seismic tremor increased at 14:49. From here.