That isn't an oven oscillator. The crystal touching the case would loose too much heat, and would make a lousy oven oscillator.
Check the frequency. If the frequency is 20 - 40 ppm high at room temperature, that would indicate an AT cut crystal oven oscillator. 10 - 30 ppm low at room temperature would indicate an SC cut crystal oven oscillator. I guess that the frequency will be very close to correct.
The crystal is in a glass housing, an HC-26 one. Those are seriously expensive, and along with the obvious complication of the circuit makes me think that it is a TCXO. I can't place the PLCC IC, but I suspect that it might be one that was specifically designed for TCXOs. Plessey, I think it was, made one that used analogue multipliers to create the cubic correction that is needed for AT cut crystals. The coefficients were set digitally for ease of setting, but the multiplication was analogue to avoid switching noise and for ease of setting.
Some TCXOs in that package needed an external potentiometer to trim to the correct frequency. It is very rare to have separate oven and logic supplies on that 5 pin layout.