Here is a link to recent review of strength training for runners.
https://www.ncbi.nlm.nih.gov/pubmed/29249083
In general here are a few "rules":
1. Muscle strength: Lower reps (less than 5) seems to favour absolute strength versus mid (10-15) or high >20 reps.
2. Muscle size: number or reps doesn't seem to matter. Someone referenced Bret Contreras and his work with Brad Schoenfeld support this. Meaning just train a movement and try to come close to muscle failure.
3. Frequency: 2-3x/week seems sufficient. More is not better.
4. Go to failure? Not necessary for the most part but you should get close. Meaning you have 1-2 Reps in Reserve (RIR). Meaning, you can't do much more than 1-2 more. However, some studies suggest if you aren't doing a lot of volume (e.g 1-2 sets) you might want to go to failure.
5. Improvements in running economy: Most strength studies suggest you can see improvements between 2-5% in running economy. What is unclear is whether it is better to take the extra time strength training and just run more. Some studies suggest that strength training might be a better choice if you are already running a lot.
6. What is BEST for runners aka why does strength training help performance? We don't know yet. We think that increasing tendon stiffness or passive joint stiffness is important. To get this we need to train heavy (>70% of max or 12 or less reps). So to cover all your potential bases it seems that you might want to:
- train 2-3 days per week
- basic compound exercises for the entire lower limb (squats, deadlifts, hip thrusts and calf raises)
- do 1-3 sets of each
- do 4-12 reps for each set
- train close to failure
Good luck,
P.S you can also try plyometrics which so similar improvements in economy