Because of its semi-firm texture, halloumi is prone to sticking to the grill. Be sure to oil the grill grates well before adding the brined Cypriot cheese.
Preheat grill to medium-high.
Zest half the lemon into a large bowl. Stir in oil, garlic, oregano, ground pepper and a pinch of salt. Add corn, zucchini, onion, bell pepper and halloumi and gently toss to coat. Cut the lemon in half.
Oil the grill rack. Reserving the marinade in the bowl for the sauce, transfer the vegetables and halloumi to the grill. Grill the corn, zucchini and onion, flipping frequently, until tender and charred in spots, 8 to 10 minutes. Grill the bell pepper, halloumi and lemon halves, flipping once halfway, until browned, 2 to 4 minutes. Grill tortillas, flipping once halfway, until lightly charred, about 1 minute.
Transfer the vegetables, halloumi and lemon to a cutting board. Cut the corn kernels off the cob. Coarsely chop the zucchini, onion, bell pepper and halloumi. Cut the lemon into wedges. Whisk sour cream and the remaining pinch of salt into the remaining marinade. Serve the vegetables and halloumi in the tortillas with the sauce and lemon wedges