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In a right cylinder the generators are perpendicular to the base; in an oblique one they are not. The bases are still circles, but the apparent outline is no longer a rectangle. If the bases are perpendicular to the axis, being inclined they look like ellipses in both views; if they are horizontal, like circles in the plan and segments in the elevation.
Both bases are circles perpendicular to the axis; being inclined to the projection planes, they look like ellipses in both views. The generators join corresponding points and are no longer vertical.
The oblique cone is solved the same way: its apex is not at the centre of the base, and the outline is drawn tangent to the base from that apex. If the cylinder has horizontal bases (resting on one of them), the outline is drawn tangent to the two circles of the plan.