First, oscillator design is a book-length subject. In fact, general oscillator design is a book-length subject, and then you can branch off and write a book just about high-precision crystal oscillators, another one about LC oscillators, yet another one about power oscillators, and all the while the folks at NIST have an entire library of journal articles on precision time keeping. So this answer is necessarily short.
The short, practical answer to your question about what frequency an oscillator will operate when it has multiple possible modes of oscillation is -- whichever one you don't want. Unless having it stay steady at one or the other would be OK, in which case it'll shift from one to the other, unpredictably.
It is even possible to an oscillator oscillate at two widely different frequencies simultaneously. It's called squegging. This is generally easier to do when you're trying to optimize the oscillator for some parameter or another, rather than when you actually want it to squeg.
The way that you determine what frequency an oscillator will oscillate at is to use Bode-plot analysis (or root-locus, if you're crazy). Model the oscillator as an amplifier by breaking the signal chain at some point and finding the gain and phase as a function of frequency from the input to the output. For most normal circuits, oscillation will happen if there's a point with zero phase shift and greater than unity gain. Again for most circuits, the action of oscillating will change the operating point of the oscillator to bring the gain at zero phase shift to unity.
If you do this analysis and you find two points of zero phase shift and greater-than-unity gain, then it is going to be very difficult to predict which frequency the thing will oscillate at. Usually, the oscillator will start oscillating at whichever zero phase shift point has the most gain and will continue there. However, if the higher-gain frequency loses gain faster than the lower-gain frequency as oscillations build up, the oscillator may switch modes. Sometimes the oscillator will start oscillating at the lower gain frequency. Sometimes each turn-on event of the oscillator will be a roll of the dice, and you'll end up with whatever frequency it was in the mood to deliver that time.
For these reasons (unless you're purposely designing an oscillator to squeg), you really want to avoid this situation.