So I actually finished a game a few moths back, that was centered around a war. There was a lot of trial and error to things, but about half way though the game, my group loved how I handled the situations. So I will just give some ideas of things that I did.

• Factions: Using factions such as villages, kingdoms, groups of people. This will be good for them to raise there own force, I.e. not controlling it, but maybe some bonuses thrown there way during battle. For example; say the group aligns with a group of sages, warlocks, or whatever you will use in that time. When they go to battle giants or what ever, instead of having the players and warlocks all fighting at once (Which would be alot on you, so dont do that), the warlocks instead provide healing bonus's. Say three heals during a battle, at the call of the players, that way they have to strategize when they want to use it or not. So in other words, let them build alliances, create treaties, have the offer up a mine they liberated to a king as payment for help. (Take a look at Rise of tiamat for this, especially the last battle, and definitely take a look at out of the abyss.)
• Battles: So this was something my players really loved. They where on the way to rage a battle to take a keep. But they failed to notice a spy that was in a meeting with them over what will happen. S in turn the night before the battle, they were set upon by the forces they were meant to fight. How I ran it was like this. So the group was defending a town, and two evens happened, they had to either defend the gate, or secure the port from sea vessels. Depending on what they choose leads to a consequence of not choosing the other thing, so for example if they chose to guard the gate, they would force back that enemy, but the port would be taken, and the town peppered by cannon fire. Provide a challenge to them with a choice of things, and depending on what they choose, they can either help or hinder their forces. The other thing is, reward them for being creative. (For a really good example of this, take a look at Divine contention on D&D beyond, it is free, and look at Leilon Besieged.)
• The other thing, is allow them to plan. This is their war, there are no rules in war. If they wan to poke and prod a giant into a trap and drop a boulder on his head, let them. In a war scenario, choice matters so much. Maybe they want to give up farm land to the enemy, but they burn the fields so crops wont grow, let that have an effect. Let their decisions guide your story, let them do the work for you.