10 seconds / year is 0.3 parts per million error (or as the time-nuts would usually put it, an error of 3 * 10^-7). A decent watch crystal is usually specified as +/- 20 ppm (2 * 10^-5), which is far worse than what you're asking for. The higher-frequency crystals used for clocking CPUs are usually worse than that.
Temperature-compensated oscillators (TCXOs) are better, in the 10^-6 range, but still worse than your spec.
Ovenized oscillators (OCXOs) can be better than 10^-7 but require watts of power, likely more than you can afford running on battery.
The Vref pin is the voltage with which the electrical tuning voltage is in reference to. So if you were applying a voltage to the tuning pin...well, no, you probably weren't. You'd need to connect Vref to the ground with which that voltage is in reference to for there to be a tuning voltage present.
Without the complete datasheet, it's impossible to be sure if it is safe to leave either of these pins floating. I would short them to each other if unused, and possibly ground them as well, though it is unlikely that is necessary. As the tuning voltage is ±5V, that would mean that a potential of 0V (like if pins 5 and 6 were shorted) is the 'neutral' or 'center' of the tuning range. From here, pin 6 can vary between -5V and 5V, pulling the frequency 500ppb faster or slower.
Of course, all the really interesting things you might use that fine bit of kit for would probably benefit from the ability to use those pins.
That thing has 5 ppb (parts per billion, aka \$10^{-9}\$) stability, which even today is excellent. You'd be hard pressed to find a similarly performing OCXO today for less than $100. Great find! If you want a good idea of all the cool stuff you could potentially use it for, just skim (at random, really) some of the recent Time-Nuts mailinglist archives. Sister list to my bros, Volt-Nuts, these are other like-minded individuals with a passion for precision. I admit the format is a bit dated (mailing list instead of a proper forum) but the archives work almost as well.
Or, if this idea appeals to you, you could always just write the mailing list about your new OXCO - I'm sure they'd be thrilled to help you figure out a project both interesting to you, within the realm of possibility to achieve (some suggestions in this kind of precision metrology hobby can have...unrealistic ideas about personal income investment), and perfectly suited to your OXCO.
Or, if you aren't that interested, you might consider putting it on ebay. These things retain their value, you'd get some dosh for it certainly. But if you are interested in this sort of thing, by all means, build something cool with it. Personally, I think its a great hobby - and one that is easy or as challenging as you make it.
Regardless, have fun. Good call on looking through that old gear before tossing it.
Best Answer
Only temperature is actively controlled. Usually OCXO and XO (and TCXO) units are hermetically sealed so humidity is not a factor.
All oscillators and crystals are designed to have little effect from barometric pressure changes and forces on the leads.
Edit: @Enerwal makes a good point about the crystal cut. Apparently SC ("stress compensated") cut crystals are most used for OCXOs, as well as IT cut. Here is a comparison of the SC cut against the AT cut more commonly used for non-ovenized oscillators. From this source is a comparison of the temperature sensitivities (graph below) but there are other important differences such as aging and drive sensitivity and pressure sensitivity.
They appear to be better in many regards, but have an unwanted oscillation mode that needs to be suppressed by the circuitry, require vacuum in the cavity and are generally more fussy and labor intensive to produce, thus more expensive. They are less pullable (higher Q), which means they have to be trimmed to a tighter tolerance.
Of course aging is accentuated in OCXOs that have an high internal operating temperature.