Heat oil in Dutch oven over medium-high heat until just smoking. Add sweet sausage links and cook until well browned and fat begins to render, about 8 minutes. Using slotted spoon, transfer sausage to paper towel-lined plate to drain, then place in slow-cooker insert. Repeat with hot sausage links.
Cook onion in sausage fat over medium heat until well browned, about 6 minutes. Stir in garlic and oregano and cook until fragrant, about 1 minute. Add tomato paste and cook until paste begins to brown, about 5 minutes. Stir in wine and simmer, scraping browned bits from pan bottom with wooden spoon, until wine is reduced, about 3 minutes. Transfer to slow-cooker insert and stir in diced tomatoes and tomato sauce.
Submerge spareribs and flank steak in sauce in slow-cooker insert. Set slow cooker on low, cover and cook until meat is tender, 8 to 10 hours. (Alternatively, cook on high for 4 to 5 hours.)
About 30 minutes before serving, transfer sausages, ribs, and flank steak to baking sheet and set aside until cool enough to handle. Shred ribs and flank steak into small pieces, discarding excess fat and bones; slice sausages crosswise. Use wide spoon to skim fat off surface, then stir sausages and shredded meat back into sauce. Stir in basil and season with pepper. Serve over hot, cooked pasta, like penne. (Left over gravy can be stored in airtight container in refrigerator for up to 3 days.)