Can I use a series crystal in an parallel crystal optimized oscillator?
If you use a series mode crystal in a parallel mode oscillator the frequency will be slightly higher than shown on the package.  As shown in this graph the reactance of the cystal varies rapidly with frequency and the frequency of oscillation the actual frequency will depend upon the characteristics of the amplifier making up the oscillator and will be such that the normal oscillation criteria are met (i.e. 360 deg phase shift and unity gain).


Even though it is a series crystal you should use the capacitors to ground at each end or it may not oscillate, I would use something like 22pF.  You are probably lucky that the stray capacitance to ground is enough to provide the phase inversion needed for the circuit to work.

If you look at simplified schematic you can deduce the type of oscillator. An oscillator for a parallel resonate crystal will be inverting (i.e. have 180 deg phase shift) and uses the crystal and the associated capacitors to provide the additional 180 deg phase shift needed for oscillation.

As far as I know all oscillators built into MCUs are designed for parallel crystals.

Also if the data sheet specifies any capacitors from the MCU pin to ground that also implies an oscillator intended for parallel crystals; series resonant oscillator circuits do not need them as they need a low impedance input and output from the oscillator.

Example oscillator: