The conflict you are facing is that between the classical and quantum pictures of the atom. Classically, the electrons orbit the nucleus, and this picture is good for some things but it is not correct. The problem is orbiting electrons are constantly accelerating, which would cause the electron to lose energy and crash into the nucleus. Since we do not observe this, something else must be going on.
This brings us to quanum mechanics. The pictures of the probability clouds you have supplied are from quantum mechanics. It shows where electrons in that orbital (confusing terminology here) are most likely to be found, but the electrons are not actually in orbit around the nucleus. In fact the electrons have no definite position unless they are measured to be at some position. These orbitals are discrete with specific energies. We resolve the classical issue in quantum mechanics. The s1 orbital is the lowest energy level the electron can be in, so it can't lose any more energy and crash into the nucleus.
So to answer your question, in the p orbitals (or any orbital really), the electrons are not actually in orbit at all.