Heat grill to medium (350° to 450°). Brush steaks with 2 tbsp. oil and season with 1 tsp. each salt and pepper and the paprika. Grill steaks until done the way you like, turning once, 10 to 12 minutes total for medium-rare; transfer to a cutting board and let rest a few minutes.
Toss avocados in a large bowl with onion, cilantro, remaining 2 tbsp. oil, the lime juice, jalapeño, and remaining 1/2 tsp. each salt and pepper. Slice steaks across the grain and serve with salad and tortillas.