Man, those are some lofty goals - not one in particular, but the combination of all will definitely be a challenge. But, you can do it if you focus your mindset on the goals.
I wouldn't recommend focusing on any specific goal for 3-6 months straight. If you do, you'll lose the other qualities. Focus on maximal strength, strength-speed, and hypertrophy (medium rep) ranges for your upper body. Don't perform any endurance work except for active recovery sessions.
Your lower body goals will be the toughest obstacle. What's your current squat and dead? If you're far from your goal, you should nix running, altogether. Focus on all strength building elements for the lower body: maximal strength, strength speed, speed strength, etc. I wouldn't recommend the running portion of your goals until you've met your dead/squat goals. Once you meet them, start running because it's much easier to run a 5K in 20 minutes, then to squat and dead the numbers you're mentioning (well, if they're raw lifts).
Bottom Line: You must reach your strength goals first, then start your running plan. You'll lose lower body maximal strength once you start running, but you'll be able to re-gain it quickly if you've already achieved the numbers.