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.
Assemble sliders with a hot meatballs, 1 tablespoon jam and a slice of smoked cheddar per bun, securing each with a wooden pick.
Bring a large saucepan of water to a boil. Using a paring knife, cut out the stem end of each tomato, then slice a shallow X in the bottom.
Plunge the tomatoes into the boiling water until their skins loosen, about 30 seconds. Remove them with a slotted spoon and let cool. When cool enough to handle, slip off their skins. Discard the water, but save the saucepan for cooking the jam.
Halve the tomatoes at their equator and gently squeeze out the seeds and juice. Cut the tomatoes into 1/2-inch (1.5-cm) pieces.
Return the tomatoes to the saucepan and stir in the sugar, pepper, and salt. Cook over medium heat, stirring frequently to ensure that the mixture is cooking evenly, until most of the liquid has cooked off. If foam occasionally rises to the top, skim it off with a large spoon. Remove from the heat and stir in the lemon juice.