Just a bit of actual sports science to dispel a few misconceptions.
The definition of strength is the ability to exert a maximal force in one effort. Based on the priciple of specific adaptations for imposed demands the way to train for maximal strength is to minimise the reps and maximise the weight/resistance.
Any activity that lasts for more than 3 minutes, is continous in nature and uses large muscle groups will be predominately aerobic (with oxygen). As all fell racing fits the criteria the important components of fitness are muscular endurance and cardio vascular fitness. This is no revelation as if your any good you will have trained this way.
However improvements in power and strength can have a positive knock effect for fell running performance in two important ways.
1 - Certain phases of the race will require anaerobic (without oxygen) performance. A sprint or short burst/effort will rely more on power and strength as it utilises alternative anaerobic energy systems.
2 - Higher levels of strength and power can improve your muscular endurance as a result of raising the upper ceiling of performance. If you think of your fitness as a pyramid with the base being provided by aerobic training and the tip being provided by strength and power.