For example left elevator angle = +30 deg, right elevator angle = -30 deg. Would these settings be able to induce a rolling moment on the aircraft? What would happen with the pitch?
This would be an elevon application (ailerons + elevator). Found on flying wings and deltas. Theoretically possible on a standard tail.
With elevons, one up and one down will roll the aircraft with out pitching it. Interesting that this can be done from the front, back, or center of the aircraft.
Someone may wish to correct me, I believe Burt Rutan put both elevator and aileron function in the canard of one of his planes to simplify the control linkages.
So, as a designer, yes this is possible.
To supplement Robert's answer, this arrangement is used not only on flying wings, where it is indeed ubiquitous, but on many more 'classical' designs.
On flying wings these surfaces are called 'elevons', but in other cases they would be termed 'differential stabiliser'.
Primarily they are found on supersonic swing wing fighter aircraft: F-14, Tornado, MiG-23, -27. The latter, for example, has flaps occupying all its trailing edge, and entirely relies on differential stabilisers and spoilers for roll control. But even non-swing-wing designs (e.g. MiG-25, Su-27) use differential stabilisers to augment roll control (sometimes only in some flight regimes).
Like with any combined control (for example, V-tail), if you use one channel (say, roll), you reduce capacity in the other. This has to be accounted for in the design, typically with increased deflection range and/or surfaces area. But there is no particular difficulty with zeroing the effect in the opposite channel: that is, in most cases deflecting symmetrically ±10° (30 is perhaps too much) will produce roll but no pitch.