In a large bowl, combine beer, lime juice, orange juice, red onion, soy sauce, olive oil, paprika, oregano, salt, garlic powder, pepper, orange slices, and lime slices.

Cut steak into sizes you can manage on the grill. Add steak to marinade and stir to mix well. Cover bowl and refrigerate at least 2 hours to overnight.

Preheat a grill for medium-high heat (350° to 450°F). (You can also use a grill pan on the stove.) Lightly oil cooking grate, using tongs and a wad of oiled paper towels. Grill steak with the lid closed, turning it once, until edges are charred and meat is done the way you like, 7-15 minutes total, depending on the thickness of the meat (medium-rare is 130° to 135°F on an instant-read thermometer and medium-well is 145° to 155°F).

Transfer steak to a cutting board and let it rest about 3 minutes. Meanwhile, grill green onions, turning them often, until lightly charred, 3-5 minutes. Transfer to cutting board. Thinly slice steak across the grain. Serve meat with onions, tortillas, salsa, radishes, and lime wedges.