You can use Fold to extend ubpdqn'subpdqn's use of Complement and Union. Pre-sorting the lists isn't necessary, especially if they are already sorted, but it ran slightly faster on large random lists.
list1 = {2, 5, 10, 11, 12, 17, 18};
list2 = {5, 8, 11, 16, 19, 21};
list3 = {5, 8, 9, 11, 16, 19, 21, 23};
lists = {list1, list2, list3};
Reap[Fold[(Sow @ Complement[#2, #1]; Union[##]) &, {}, Sort /@ lists]][[-1, -1]]
(* {{2, 5, 10, 11, 12, 17, 18},
{8, 16, 19, 21},
{9, 23}} *)
Comparison with and without Sort:
Block[{lists},
SeedRandom[1];
lists = Table[RandomInteger[2 * 10^5, RandomInteger[{10^3, 10^4}]], {200}];
Reap[Fold[(Sow @ Complement[#2, #1]; Union[##]) &, {},
Sort /@ lists]][[-1, -1]] // Last // AbsoluteTiming
]
(* {0.951474,
{130, 8034, 9175, 19773, 23884, 25942, 32039, 35681, 43301,
48881, 55009, 55076, 59170, 60909, 74140, 75298, 79379, 84588,
96241, 100238, 101899, 104788, 106787, 109378, 110730, 118780,
120469, 121675, 124215, 129721, 130787, 136182, 137604, 138686,
143374, 152045, 161277, 169106, 171461, 188972}} *)
Block[{lists},
SeedRandom[1];
lists = Table[RandomInteger[2 10^5, RandomInteger[{10^3, 10^4}]], {200}];
Reap[Fold[(Sow @ Complement[#2, #1]; Union[##]) &, {},
lists]][[-1, -1]] // Last // AbsoluteTiming
]
(* {1.009209,
{130, ..., 188972}} *)
