Does neural oscillation happen at the same frequency in all parts of the brain simultaneously?
Neural oscillations occur on both a cellular level and on a macroscale level, the latter usually referred to as brain waves.

Looking at macroscale brain activity and particularly brain waves is often done via EEG, which has poor resolution and suffers from attenuation. EEG activation is really due to huge numbers of neurons. Hence, it represents a very coarse, averaged view of the current activity. So, even when the EEG shows nice smooth variation, the individual neurons are far from it! Of course, more recently, using other methods (e.g. fMRI) has become more common. 


  My question is are all parts of the brain firing off at the same frequency at any given time or are some parts for example operating at a delta frequency and others operating at alpha frequency? Do different types of brainwave occur simultaneously or is always all of the brain operating at one frequency?


No, as I said, most studies look at the cortical areas specifically. But even within the cortex, the brain activity is very complicated, and certainly not subscribing to any one frequency. (In fact, when this hyper-synchronization happens, it is called an epileptic seizure! e.g. see Garcia-Hernandez et al, Understanding synchronization and hyper-synchronization in the the septo-hippocampal system). 

In any case, imagine brain activity being measured over time. We then look at the frequency components (e.g. via Fourier analysis). See e.g. Gross, Analytical methods and experimental approaches for electrophysiological studies of brain oscillations for details. Notice these methods usually give the "strength" of the activity across the frequency spectrum. When there are brain waves, we are merely saying that activity is concentrated in a specific frequency band. It is often smeared across the band, and activity usually exists throughout the spectrum. 

It also depends on spatial resolution of the frequency analysis. Some studies look at, say, just the Hippocampus. So yes, it is quite possible for some of the brain to operate at one frequency, while others operate at another. Or one could average over the whole cortex. It depends on the study! 

So pretty much in all cases, everything is more heterogeneous than you might think.

Some literature to read:


Breakspear, Dynamic Models of Large-Scale Brain Activity
Varela et al, The Brainweb: Phase Synchronization and Large-Scale Integration
Salinas et al, Correlated Neural Activity and the Flow of Neural Information