You can maintain strength in two ways:
1. Do each strength move at least once a week. You can do this either in the 3x5 or 5x5 strength method, or
2. You can do these moves at 50-75% 1rm in a medium to heavy metcon WOD, and knock out your conditioning.
Now if you do Crossfit Endurance, you should be able to maintain your strength while preparing for your run race. Just minimize the longer runs (3-4 longer ones before race day, the rest only sprints as prescribed by CFE). Don't forget to do the actual CrossFit wod prescribed by CFE. That's what will allow you to maintain your strength and strength endurance.
For the OP, look into CrossFit. Do strength and heavy metcon work when you can get to the gym, and do the other metcons at home. Consider investing in a door pull up bar and some hand weights (at a minimum). With those items, you can do many different WOD's.
A good schedule would look like this:
Day 1-Squat, then Bench OR shoulder press (alternating weeks). Short but heavy metcon (if you want)
Day 2-Metcon at home (15-20 min)
Day 3- Off
Day 4- Deadlift or clean (alternating weeks). Short, intense, heavy metcon.
Day 5 -Heavy metcon in gym or skill based metcon at home (handstand pushups, L pullups, Muscleups (if you have rings),
Day 6- Long metcon at home or heavy metcon in gym. Can also do a third strength workout here (Cleans or DL, or a front squat or OHS)
Day 7- Off
Finally, you can consider accumulating equipment for your garage and do this at home. Then there are no excuses.