Heat a grill to medium-high heat (400° to 500°). Run a metal skewer through each onion slice to hold it together. Brush onion slices and corn generously with oil.
Lay onion and corn on cooking grate (close lid if using gas) and grill, turning as needed, until lightly seared with grill marks--the onion on both sides, the corn all over--10 to 12 minutes total. When cool enough to handle, chop onion and cut corn kernels from cobs.
Mix onion, corn, tomatoes, slivered basil, lemon juice, 1 tsp. salt, and 1/2 tsp. pepper in a bowl.
Brush salmon pieces on both sides with oil. Sprinkle flesh sides with salt and pepper. Lay flesh side down on cooking grate (close lid if using gas) and grill, carefully turning once with a wide spatula, until just opaque but still moist-looking in center of thickest part (cut to test), 9 to 10 minutes total.
Mound relish on plates. Lift salmon off skin with spatula and set alongside relish. Garnish with lemon wedges and basil sprigs.
Note: Nutritional analysis is per serving.