What type of oscillator is this? (Theremin Project. Variable Pitch / LC Oscillator)
The oscillation frequency is determined by C1 and L5: -

\$f_O = \dfrac{1}{2\pi\sqrt{LC}}\$

And, for values of 3900pF and 100uH, it should oscillate at 254.8 kHz theoretically but there will be parasitic capacitance in the inductor and miller capacitance in the transistors that make the actual capacitance bigger hence lowering the resonance to 236kHz.

I'd call it an LC oscillator.