I simulated the oscillator portion (without the varicaps), using 100uH and 100pF, and 1uH and 10pF. It oscillates. and the tank has a nice sine wave, but unless you want some serious harmonics (which may be the case?), I would not take the output off the emitter of Q7.
You would need a separate emitter follower off the tank for a good sine wave. A direct-coupled PNP would work well with the voltages present in the circuit.
I just used 3904s and a 3906. Lower-capacitance transistors would be better, especially with the added capacitance of the PNP.
I am attaching the .ASC file, in case someone wants to run the sim in LTspice.
EDIT: I changed Q3,4,6, and 7 in Othello's schematic (Q1,2,4, and 5 in mine) to MPSH10, and the PNP follower to MPSH81. Much better at high frequency than with the 2N3904s!