Tilted oil-water contacts resemble the Loch Ness monster. Some people claim to have seen one, but most people are skeptical they exist at all. I agree with both.
Titled contacts shouldn't exist in an idealized, normative reservoir. They certainly can exist in a few, rare geologic circumstances, but they don't exist in the way you probably think.
Among the three forces in a reservoir, gravity is generally the strongest, and certainly at discovery. Of course, gravity makes contacts flat through a medium continuous permeability and constant properties. To overcome gravity in a virgin reservoir would require a natural pressure gradient, a massive and continuous flow of aquifer water through one side of the aquifer, to create a pressure drop sufficient to overcome gravity and to create a stable, tilted contact. Perhaps such could exist in theory if the aquifer is connected to the surface, though, in reality this hypothetical just doesn't exist.
To create a genuine "tilted" oil-water contact, the nature of the rock or the fluids must change around the contact, but Occam's razor suggests looking at more likely causes.
The changes, though, can be difficult to spot. Most apparent of the causes, though still not obvious, is a tar mat. Occasionally a layer of asphalt or tar will form at an oil-water contact before additional tectonic tilting of the structure. The tar mat plugs the pore space and forms a barrier to upward movement of water during the additional tilting. Prudhoe Bay field and the west side of the Hawkins field have such tar mats.
The second cause is even less obvious: differential diagenesis. The emplacement of oil or gas in a trap arrests diagenetic changes related to formation water. The water no longer flows through hydrocarbon-saturated rock, but changes can continue in the water-saturated volume. For example, chlorite overgrowths can form or continue to grow in the aqueous environment but not the oil rim. As long as the structure remains undisturbed, the differential diagenesis has no affect on the contact. If, however, the whole structure is subsequently rotated, then the re-leveling of the contact is impaired by different capillary pressures above and below the paleo contact. This kind of dynamic has been observed, for instance, in the Delaware Mountain Group of west Texas.
(Similarly, it may also be possible for different capillary pressure character in different rock facies to create an unlevel surface of high water saturations, even if the level of zero capillary pressure is constant. In this case, the question becomes the definition of "oil-water contact." Different parts of our industry use three differentiable definitions.)
Other cases, though, give the false impression of a tilted contact, and these are more more common than a genuinely tilted contact. Water influx from early production can raise a contact. Contacts can be terraced when divided by faults or interbedded shales. In one case I've seen, a subseismic fault divided the oil rim but still allowed communication between both sides in the gas cap.
Perhaps most easily, a modest error in a measurement can make cause a level contact to appear at different depths. Errors can come from kelly bushing elevation (such as different rigs having been used for drilling wells), directional survey (different methods and low resolution surveys can move the location several feet), or errors in measured depth indicated by the logging company.
When you think you see something as odd as a tilted contact, the first place to look is for the obvious and common explanation. However, if it really is tilted, then the differences in contact depth offer a clue to larger and more important dynamics in the reservoir.