Strategy for Spanish Civil War
Start out by sending all of your garrisons to the provinces around Seville, so you can bring your mobile troops north to face the Nationalists. Also send your navy to the Baleric Islands to maintain your toehold there. Remember that you won't be producing any more units or getting reinforcements, so what you have is what you get.
The best strategy in the north is to link up with Oviedo and try to surround Burgos and La Coruna. If you capture La Coruna, then other Nationalist areas will be cut off from supply. Your infantry should be put into the push in the north, while your tanks (they're not much good in the mountains anyway) hold the line north of Madrid.
Generally, the Nationalist strategy is pretty straightforward: sever Oviedo from the rest of Republican territory, capture Madrid, and burst out from Seville. The trick is to maintain the initiative, focusing on one front at a time to keep the Nationalists from doing what they do best. Also, because you'll be using most of your military on the front, it may be a good idea to do whatever necessary to prevent the two revolts which will inevitably happen (although I allowed the Basque revolt because I had troops in that province, but I wouldn't recommend relying on chance to avert revolt).
After conquering the north, focus on taking out the remaining Nationalist pockets. The unfortunate result of winning the northern war, however, means that you have to either rapidly capture Seville (the new Nationalist capital) or wear them down in a war of attrition. If you can't take Seville right away after defeating the Nationalists in the north, don't bother. It’s better to just take their remaining VPs in Africa and the Balerics and settle for your marginal victory than to hammer away and let them keep everything else (and be bored for the last month or so of the scenario).