If there were to be an explosion in space, given that space is a vacuum and oxygen is absent, what would happen?
There are several types of explosion which can occur either in space or in an atmosphere.
An explosion is a rapid expansion in volume along with a rapid release of energy. There are several types of explosion.
A container which has its contents at a higher pressure than the outside of the container can explode if the container ruptures.
Chemical explosions occur when high speed chemical reactions occur which release a lot of energy. Some chemical explosions involve combustion in oxygen. These don't make direct use of atmospheric oxygen, rather oxygen has to be mixed in with the other ingredients in the right proportions. Flammable gasses can explode if mixed with oxygen. Other explosives contain oxygen rich compounds such as nitrates.
Atomic bombs work by triggering a fission chain reaction.
Explosions in air generate shock waves in the air which can themselves be damaging and cause the sound. When something explodes in space the material simply expands out indefinites until it is dissipated.
The fact that there is no oxygen in space has no effect because oxygen has to be part of the explosive material if required.
The biggest explosions occur naturally in space in the form of nova and supernova explosions. These occur when a significant amount of a star's material undergoes fusion reactions in a short period of time.