Strength training can produce improvements in upper and lower body extremities, which will intern improve running economy and a decrease in steady state oxygen consumption. This means the runner should be able to run faster over the same distance.
Plyometrics have been recommended for cross country skiing and there are numerous exercises such as single and double leg hops and bounding which are also good for cross country running. Plyometrics develop explosive power, which means you are able to get from point A to point B faster than your opponent. This means movement in all directions, such as vertical jumps, forward jumps and sprinting.
The principle of specificity is important because it is most effective when the actual training activity such as running is similar to the "target" activity such as cross country running. The best method of training here is to perform strength training activities at the highest possible speed of movement. An example would be running...uphill as fast as possible for as long as possible with resistance. The athlete could wear a weight vest, have a parachute attached to his/her back or a partner holding resistance bands around the waist.
Olympic style lifts offer the athlete a more optimal velocity profile as compared to traditional strength training exercises such as the squat. That makes it an effective training strategy for any sport that requires explosive power. The best strategy however is combining what we call a "mixed methods training strategy" that incorporates maximum power training and plyometrics which will optimally develop the best cross country runner.
Another component for cross country runners to consider is what exercises closely resemble the biomechanics of running as compared to strength training exercises. The back squat for example occurs mainly in the vertical plane of motion. In contrast, single leg hops are more mechanically similar to running because they are performed in the horizontal plane of motion similar to running. Also keep in mind that when the athlete runs in a cross country event, the foot strike is a unilateral event. In other words, one leg touches the ground at a time and one leg works when one leg is airborne. Therefore, the athlete should consider incorporating as many movements similar to a unilateral foot strike as possible. Such examples are single leg hops, single leg box jumps, single leg push offs and alternating leg push offs.