Combine olive oil, balsamic vinegar, garlic, oregano, salt, and pepper in a shallow dish or ziplock bag. Add chicken breasts and turn to coat evenly. Let marinate for 15-30 minutes at room temperature (or up to 4 hours in the refrigerator if preparing ahead).
Whisk together balsamic vinegar, olive oil, honey, Dijon mustard, salt, and pepper in a small bowl until well combined. Set aside to allow flavors to meld.
In a dry skillet over medium heat, toast almonds until golden and fragrant, about 3-4 minutes, stirring frequently to prevent burning. Remove immediately from hot pan to cool.
Preheat grill or grill pan to medium-high heat. Remove chicken from marinade and grill for 4-5 minutes per side, or until internal temperature reaches 165°F (74°C). Let rest for 5 minutes before slicing.
Arrange spinach in a large serving bowl or individual plates. Top with sliced strawberries, red onion, feta cheese, and toasted almonds. Add sliced grilled chicken and drizzle with prepared dressing. Garnish with fresh basil.