I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.
The weak force "looks" different because in the first (and still most important) reincarnation we have encountered it - namely beta-decay (including the decay of the neutron) - the force seems to be a contact interaction: it has an extremely short range, essentially zero.
However, any phenomenon that differs from the indefinite existence of an object that moves in the same direction by the same speed forever requires a force to be explained. The force required for the beta-decay is the weak nuclear force.
While the decay seems to "directly" transform a neutron into a proton, electron, and antineutrion, a closer investigation of the force that began in the 1960s has demonstrated that this force is actually analogous to other forces, including electromagnetism, because its range is finite (nonzero). It's only limited because it's mediated by the W and Z bosons which are, unlike photons, massive. So the force doesn't get "too far".
However, in our modern description of the forces, electromagnetism and the weak force have to be described by a unified "electroweak" theory and they mix with one another. At distances much shorter than the range of the W/Z bosons, the electromagnetic and weak forces become equally strong and, in some proper sense, indistinguishable.
I would actually emphasize the difference between the forces, rather than the similarity. Although we (as theorists) like to bundle the whole shebang into a "neat" $U(1)\times SU(2) \times SU(3)$ gauge structure (and possible some gauge version of gravity), it doesn't mean that reality has to be that neat (e.g. chirality of electroweak, neutrino masses, etc.)
- Electromagnetism is long ranged, and drops off in strength with distance.
- Strong force is actually also long-ranged, but gets stronger with distance! This causes the side effect that trying to separate a pair of opposite charges causes pair creation, and so we always see neutral composite particles.
- Weak force is intrinsically short ranged (order $1/M_W$), and primarily it does not transmit a force --- but transmutates particles. Electrons go to neutrinos, quarks mix, etc.
And for gravity, say whatever your favourite quantum gravity picture say it is :-)