I'm no expert when it comes to balancing mechanics, but this class does seem a bit too powerful. At 2nd level using a longsword, I can use Shocking Grasp to essentially do 3d8 (plus ability mod) damage per turn at no cost, which seems a bit much. Furthermore, if the enemy is wearing metal, then I get advantage on the attack rolls and don't have to worry about provoking opportunity attacks afterward.
Or if I'm wanting defense, I can just shocking grasp the dude and then cast Blade Ward to, as aforementioned, get essentially perma-rage.
Also, while I find it to be somewhat more balancing, I believe there are very few offensive spells with a range of touch, which makes the Spellstrike ability slightly limiting.
I find these possibilities to be a problem mainly because they cost no resources. Sure, there are always exceptions, but it seems that by and large if I want to kill something in melee combat I can do 3d8(plus ability mod) damage each turn without sacrificing any resources starting at 2nd level, which just seems like a bit much.
That being said, I truly do love this rendition of the Magus from Pathfinder; it's the truest conversion I've ever found. It just needs a bit of work perhaps? Maybe after playtest you've updated it a bit, I'm not sure. But I'd love to see an updated version!
Something I've seen often in other renditions is the ability to use Spellstrike a number of times per day equal to the Spellcasting Ability Mod (in this case Int), which seems more balanced for 5e. But that's just an idea.