If you don't have the Wailmer Pail, it is located at the Pretty Petal Flower Shop on Route 104. Talk to the girl at the top of the room and she will give you pail.
To catch the Sudowoodo (there is only ONE), SAVE FIRST. Go to your bag, select the pail, use it, and Sudo will attack you. Use attacks that it is strong against (Fire, Flying, Normal, Poison) to whittle away its HP and then toss the Poke Ball of your choice (if it takes a long time to get his HP down, I suggest Timer Ball, but UBs will always do). The crazy petrified tree with Strongbad hands is yours.