Heat a grill to medium-high. While the grill heats, cook the pasta according to the package's directions. Drain, rinse under cold water until cool, and drain again. Reserve in a large bowl. Toss the asparagus, corn, and onion with the oil and a generous pinch of salt and pepper to evenly coat. Grill along with the sausage links, turning to evenly brown, until crisp-tender and lightly charred, about 6 minutes for the asparagus, 10 minutes for the corn, and 8 minutes for the onion. Grill the sausage, turning occasionally, until grill marks appear and heated through, and 10 minutes. Transfer everything to a cutting board. When cool enough to handle, cut the asparagus into 1-inch pieces, cut the kernels off the corn cobs, thinly slice the onion, and cut the sausages into thin half-moons. Add to the pasta, along with the sauce, and toss until evenly coated.
For Pasta Sauces: Stir all of the ingredients together (for each sauce separately) until well-mixed.
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