What type(s) of eruptions are common on stratovolcanoes?
Very explosive and life threatening types of eruptions.
Stratovolcanoes tend to form in locations where the crust is being subducted below a continent. Partial melting of the descending slab goes on at a certain depth and the lighter felsic magma starts to rise up to the surface. When it breaks the surface, a stratovolcano forms, usually in a catastrophic fashion. See pic.
This explosive nature is due to the very viscous nature of the magma - this means it is very sticky and has a tendency to cool quickly and plug up. When it does get plugged and a rising magma section pushes through, it tends to be explosive (e.g volcanoes on the west coast of North America).
This is in contrast to the more shield type volcanoes where the magma is more viscous, tends to flow easily and does not get plugged up (e.g. the Hawaiian volcanoes).