Residual dust (taking the easier one first) - volcanic ash is primarily silicates (rock, formerly molten). The specks of dust can be abrasive, sand-blasting windscreens and paint, and causing some internal engine abrasions. But their largest and most dangerous impact is that they melt again at turbine engine temperatures and thus collect in the engine as a gooey molten mass, clogging the internal airflow pathways. That is what shuts down the engines if one flies through such a cloud.
If your bolide is primarily ice or nickel-iron, the ice will evaporate in the blast and become mostly a non-issue (although, if the water vapor thus formed refreezes in the atmosphere, see the effect of high-altitude (10-15km) ice crystals on airspeed probes, Air France 447 among others). The nickel-iron will be much denser than the silicates, and precipitate to the ground fairly quickly (although how quickly is worth researching). It is the rocky percentage (if any) of the bolide that will pose the biggest threat in terms of dust or ash to aircraft.
As to aerodynamic effects of the shock or pressure waves: The two aircraft that dropped the Hiroshima and Nagasaki bombs were both tail-on to the blasts (lateral distance ~18km plus slant range), blasts ~16 and ~21 Kt. Noticeable shocks, but no airframe damage. Bockscar from Nagasaki lost its radios, but that may not have been due to blast.
Aircraft are obviously designed to face, and operate, into the prevailing "wind" or slipstream of flight. Their flight controls (rudder, elevator, ailerons, spoilers/spreedbrakes, flaps (at least simple flaps, not so sure about complex types) are hinged along the front, and free floating at the back. Thus they are susceptible to (to use the sailing metaphor) a "jibe" - or being slammed rapidly from one extreme to the other, by a wind or shock wave from the rear, and damaged or even ripped off.
One example - elevator cable separation in an Air Moorea Twin Otter, which was suspected, but never proved, to have been weakened by blast on the locked elevator from the jetwash of nearby large taxiing aircraft, while parked at an airport.
But obviously the distance involved in the WW2 bombings attenuated the blast to the extent that this did not happen to them.
Therefore, the intuitive idea that turning to face the blast source is a good one - up to a point. Aircraft are designed to withstand a much larger shock or wind from the nose than from the tail.
Aircraft toughness or tolerance to the forces in forward motion are generally described as the Vne, which is the speed (Indicated Air Speed on the gauge - minus a large safety factor) at which the dynamic pressure of the airflow may fold the wings or tailplane backwards. At high altitudes, a Mach operating limit is imposed, but that has less to do with strength (one may be well below Vne) and more to do with the creation of localized continuous shockwaves in places where funneling of the air around parts may cause the local airspeed to approach Mach 1, which can cause control problems. Not directly applicable to the passage of an instantaneous shockwave, although also worth exploring.
Aircraft "toughness" in the up/down direction (a blast above or below) is generally described in G forces. How many G can cause a wing or tail to fail, up or down. Generally, the absolute limit for commercial aircraft will be in the middle-high single digits (the rated limit much lower to incorporate a safety margin), with the positive limit being higher (since the wings are supposed to lift the plane) than the negative limit. Military jets may have +G limits reaching into double digits.