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Stir together flour, pepper, 1 tablespoon of the paprika, and 2 teaspoons of the salt in a large bowl; add beef cubes, and toss to evenly coat. Heat oil in a large skillet over medium-high. Add half of the beef; cook until well browned on both sides, about 4 minutes per side. Transfer to a 5-to 6-quart slow cooker. Repeat process with remaining beef. Reserve drippings in skillet and any remaining flour mixture in bowl.
Add onion, celery, carrots, and garlic to drippings in skillet; cook over medium, stirring often, until softened, about 2 minutes. Add tomatoes, reserved flour mixture in bowl, and remaining 1 tablespoon paprika; cook, stirring constantly, 1 minute. Transfer mixture to beef in slow cooker.
Cover slow cooker; cook on HIGH until beef is fork-tender and sauce has thickened, about 4 hours. Remove from heat; stir in vinegar and remaining ½ teaspoon salt. During final 10 minutes of goulash cooking, prepare egg noodles according to package directions. Serve goulash over hot egg noodles.