The 18,500-hour airline transport rated pilot reported that he arrived at the airport to pick-up the turbine powered twin-engine airplane that had just undergone a complete paint job. The pilot added that Jet-A fuel was not available at the airport, so he intended to fly to a nearby airport located within 30 miles to purchase fuel for the flight back to their home base. While taxiing for departure on runway 31 at the uncontrolled airport, the right main landing gear impacted an unmarked pothole, which was not visible due to standing rainwater from recent rain showers. The pilot reported that the airplane sustained quite a jolt when the landing gear collided with the pot hole; however, he continued to taxi as he monitored the brakes and tracking to make sure he had not blown a tire. The pilot did not experienced any signs of damage and continued to taxi to the runway for takeoff. Takeoff and climb were reported as normal; however, upon reaching his cruise altitude of 3,000 feet, the pilot noticed that the airplane was unusually out of trim, and the airplane required both rudder and aileron trim adjustments in order to maintain level flight. The landing at his refueling stop was uneventful. During the post flight inspection at the refueling stop, the pilot found that the airplane's right wing and right engine nacelle were structurally damaged. There were no NOTAMs in effect at the time of the mishap on the condition or status of the damaged or un-repaired taxiway.