An oblique cone is one where the vertex is not over the center of the circular base. In the figure above, drag the vertex point and note how the cone "tilts" to one side when the vertex is not over the base center point. The opposite is called a 'right cone', where the vertex is above the base center point..
In an oblique cone, the usual method to calculate its surface area no longer works. However the same method for calculating volume works for both right and oblique cones. See Volume of a Cone. You must use the vertical height h of the cone in all cases when calculating the volume.