We present the results of a photometric variability survey in the young open cluster Stock 14 and the surrounding fields. In total, we detected 103 variable stars of which 88 are new discoveries. We confirm short-period, low-amplitude light variations in two eclipsing members of the cluster, HD 101838 and HD 101794. In addition, we find two new beta Cephei stars of which one, HD 101993, is also a member. The sample of pulsating cluster members is supplemented by one multimode slowly pulsating B-type star and several single-mode candidates of this type. The other pulsating stars in our sample are mostly field stars. In particular, we found fourteen delta Scuti stars including one gamma Dor/delta Sct hybrid pulsator. From our UBV photometry we derived new parameters of Stock 14: the mean reddening E(B-V) = 0.21 +/- 0.02 mag, the true distance modulus, 11.90 +/- 0.05 mag, and the age, 20 +/- 10 Myr. Finally, we use the new photometry to analyze changes of the 6.322-d orbital period of the bright eclipsing binary and the member of the cluster, V346 Cen. In addition to the known apsidal motion, we find that another effect, possibly light-time effect in a hierarchical system of a very long orbital period, affects these changes. The updated value of the period of apsidal motion for this system amounts to 306 +/- 4 yr. The open cluster Stock 14 was found to be a fairly good candidate for successful ensemble asteroseismology.
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