Purée tomatoes with their juice, 1 can at a time, in a blender and transfer to a bowl.
Heat oil in a large heavy pot over medium-high heat until it shimmers, then sauté onion until golden, about 6 minutes.
Add garlic and sauté, stirring, 1 minute.
Add tomato purée, sugar, bay leaf, and 1 1/2 teaspoons salt and simmer, uncovered, stirring occasionally, until thickened, 40 to 50 minutes. Discard bay leaf.
Stir together bread crumbs and milk in a large bowl and let stand 10 minutes.
Add meat, garlic, cheese, eggs, parsley, oregano, 1/2 teaspoon salt, and 1/2 teaspoon pepper and blend with your hands until just combined well (do not overmix). Form level 1/4-cup portions into meatballs.
Heat oil in a 10-inch heavy skillet over medium-high heat until it shimmers, then fry meatballs, about 6 at a time, turning occasionally, until well browned and cooked through, 4 to 6 minutes per batch.
Transfer to paper towels with a slotted spoon.
Add drained meatballs to tomato sauce and simmer, stirring occasionally, until meatballs are heated through.
Assemble sliders with a meatball and 1 tablespoon sauce per bun, securing each with a wooden pick.