Why would you ever use the strategize order card? Why wouldnt you just use Mobilize or Conquer? You can move with both of them and do extra things. Is there any advantage of using Strategize while playing?

Draw more Tactics cards with the Supremacy bonus? Get heroes closer to their goals?...

Strategize is the only order that lets you move heroes. It lets you move ALL of your units and heroes however you want them to be moved and it doesn't use your activation counter so your units will be able to move and attack again this year. It could be a decent card to play in autumn if you want to spread your units out after recruiting in summer before some of them die in winter.

And since it's lower numbered than the others move cards, you get to play it before your opponents who are using mobilize or conquer even if they have more influence than you. In my last game, this allowed me to move my units to a choque point my opponent was about to move to. And on top of that it's the order to draw tactic cards, so long as you're using it in spring.

Honestly, all of the orders have their strategic use. You might not play this one as often as some of the others but it's far from useless.

Many times my first order of the game will be Strategize if I start out next to a city or a space without any neutral units in it. Strategize really shines when you just attacked someone and you left some areas uncontrolled. Play one Strategize and you can take control of nearby empty areas before Fall or a harvest order. Really, any time you want to move any/all of your units/heroes up to one space (no attacks) without activating the destination .

As mentioned in different ways, Strategize is the only way to REDISTRIBUTE your units. Mobilize and Conquer both essentially "consolidate" units, because they all have to move to the same place. Sure, you could pull them from different areas, but they can only go to a single location.

With Strategize, you can effectively take a heavily-populated area, and move units around to spread them out; like broken says, I often use it early in the game to get some new areas right off the bat, and to possibly position my heroes a little closer to their goals. Later in the game, I'll often use it after a Recruit order, and move the units around to not die in Winter.

It's trickier to use the Supremacy bonus of this one, since you only get it in the Spring (unless you have Brilliant Maneuver), and Tactics cards are nice, so if you plan right, too, you can do a Recruit the previous winter, then Strategize to position them where you want in the Spring, and get the bonus. Then you will be ready for the rest of the year.

The fact that it doesn't activate anything is also often a huge factor.

Being able to move ALL your units EVERYWHERE as needed is also something that no other Order can replicate. At best Mobilization can get close, but then those areas you moved troops into are locked down until next Spring often leaving you wide open, especially if you were consolidating/strengthening your front lines.