Driving an audio speaker design questions
Two things.

First, calculate the peak current needed to produce 1 W in 8 ohms, and compare this to the maximum continuous current rating for the opamp.  I think you will see a problem there.  While it is possible to make an audio power amplifier stage be both the signal oscillator and the speaker driver, a more conventional approach is a low-power signal source followed by a volume control and a small audio power amplifier to drive the speaker.

Second, there is a problem with the oscillator circuit.  Search for Wein bridge sinewave schematic and you will see many examples.  Most of them have a light bulb or a FET in the negative feedback loop to stabilize the output amplitude.  The problem with the circuit you have is that in order to maintain oscillation at a constant output amplitude, it needs to have a very precise gain that does not drift with temperature.  The standard solution is to add a method of using the output amplitude to control the circuit gain such that when the output amplitude increases, the gain is turned down (and vice versa).  Both TI and National Semiconductor (before they were acquired by TI) have excellent app notes on sinewave generation techniques.