Why are the IV curves of capacitors and inductors ellipses?
You are driving the L and C with a sine or cosine wave, right?

If you are driving the inductor or capaactor with a sine or cosine, the derivative terms for the inductor and capacitor I-V equations will cause more cosines and sines to pop out.

Intuitively, there is a lag time between I and V for capacitors and inductors. For L and C, one parameter reacts immediately while the other lags. The parameters are reversed between L and C so the ellipses between the two are turned 90 degrees, because the lagging parameter of one is the leading parameter of the other.

The area in the I-V loops for L and C represent the energy stored. Similarly, the area in the B-H curve also represents the energy stored. A magnetic core that stores less energy is skinnier and has less area. A resistor stores no energy so the resistor I-V loop has no area which makes it a line.

Hypothesis:
B-H curves are an ellipse that is slanted the same way the resistor I-V line is slanted, rather than vertical or horizontal ellipse the L or C (until you saturate them then they turned S-shaped which still maintains a slant). Why is it slanted?

The slant in the I-V loops might have something to do with the fact the resistor is lossy and the B-H loops is also lossy. The inductor and capacitor have no loss so the curve is perpendicular (either horizontal or vertical). The B-H loop of a magnetic core that stores little energy gets narrower and skinnier so there is less area. Although, I have seen metglas B-H loops which have very vertical edges and so don't look like they slant very much.