I'm going to assume that you used something like a breadboard to mount your components, and standard breadboard jumpers several inches long. And there lies your problem.
75 MHz is just too high a frequency to get reliable results on a standard breadboard unless you use great care. The biggest problem is the ground connection of your scope, which needs to be as short as possible, and connected to the circuit as close as possible to the ground pin of your oscillator. Just as an experiment, try looking at your oscillator output on the scope and try moving the probe around (changing the angle of your hand and probe).
Another way to look at this is to consider that your physical setup is almost certainly not exactly what your schematic indicates. Long wires will have parasitic inductances which become important at 75 MHz.
Second, especially with the oscillator, is making sure you have properly decoupled it. Use a 0.1 uF ceramic cap connected as close to the power and ground pins as is humanly possible, with the cap leads as short as possible.
Comparing your oscillator and an external function generator is fraught with possible difficulties. As a start, the FG is probably putting out fairly good sine wave. Your oscillator, on the other hand, is doing its best to put out a square wave - notice the 3 nsec rise and fall times. This will produce large signal components at multiples of 75 MHz. Granted, the large load capacitances you use will tend to filter these harmonics out, but with varying effects.
And finally (although perhaps I should have listed it as first), as asdex has pointed out, your oscillator is completely unsuited for the circuit you are investigating.
While this is not certain, there is a very good chance that you've been burned by resistor tolerance.
A Wein bridge oscillator requires a gain of 3 at the resonant frequency, and for your configuration that means a 2:1 (or better) ratio between R1 and (R2 + R2a). The nominal values you've got give a gain $$G = 1+\frac{R1}{R2+R2a} = 1 + \frac{4.7}{2.3} = 3.043$$ which provides a slight gain margin over your minimum of 3.
However, you've used 5% resistors, so the actual value of R1 could be as low as 4.465, and your R2/R2a could be as high as 2.415. This would give a gain of $$ G = 1 +\frac{4.465}{2.415} = 2.849$$ and this would explain your failure to oscillate.
Replacing your resistors with 1% units is a good idea, although it's still possible that the unit won't oscillate. If this happens, try removing R2a and see what happens. You might also measure your existing resistors and see just what values you really have (do it with the resistors disconnected from the circuit).
Best Answer
The LM358 output will swing almost to the negative power rail but will only get within about 2V of the positive power rail. So I think you are seeing clipping on the positive swing but distortion on the negative going output swing. I have tried to use that diode amplitude controlling technique before which resulted in a distorted output. I Got much better results with this J-FET based design.