toodle-oo, bye(-bye), cheers, cheerio [interjection] [‘toe-du-lu-doo-kie’] 
“Toedeledoki” is a very informal way to say (good)bye.
The use of “toedeledoki” in the Dutch language was strongly boosted by the comedy series Jiskefet, which aired from from 1990 to 2005 on Dutch
television. It was a show with various humorous and absurdist
sketches. One of the recurring sketches had three men in it with a southern Dutch accent (from the province of Brabant), sitting in the office, talking about various trivial everyday topics. One of these characters would always dump his sandwiches – made by his wife – in the trash bin while exclaiming “Toedeledoki!”
Sometimes, Dutch ‘goodbye words’ – such as “dag”, “doei” or “toedeledoki” – are used to express one’s disapproval of a certain activity or situation. See the last example.
Examples:
– “Ik ga naar huis, toedeledoki!”
(“I’m going home, bye-bye!”)
– “Mensen, het was erg gezellig, maar nu moet ik echt gaan…Toedeledoki!”
(“People, I had a great time, but I really have to go now…Cheerio!”)
– “Schat, kun jij de afwas doen?” – “Toedeledoki, daar heb ik nu echt geen zin in!”
(“Honey, can you do the dishes?” – “Forget it, I really don’t feel like doing that now!”)
Related words:
– “Doei“: bye bye, so long, ta ta, see you.
– “Tot ziens”: goodbye, bye.
– “Afscheid”: [noun] parting, leaving.
– “Iemand gedag zwaaien”: to wave hello/goodbye to someone.
– “Vaarwel”: farewell.
Extra:
Another brilliant joke from the same Jiskefet episode (at 2min09sec): “Wat is de verleden tijd van komkommersla?” – “Kwamkwammersloeg!” 😀 Ask you local Dutch Guru for an explanation…
Extra 2:
Let’s do some alternatives for “toedeledoki. Here are a few ways to say goodbye in (spoken) Dutch:
Informal
– “Groetjes!”: bye-bye!
– “(De) groeten”: bye.
– “Doei/doedoei/doeidoei/doeg”: bye, cheers.
– “(De) mazzel”: see you.
– “Toedels/toedeloe”: toodle-oo, cheerio, bye-bye.
– “Later/lator/laters”: (see you) later.
– “De ballen!”: cheers! bye!
– “(Ik) zie je”: see you.
– “Tot sinas”: (a pun for “tot ziens”) (good)bye.
– “Hoihe”: [used in the province of Limburg] bye-bye.
– “Houdoe”: [used in the province of Brabant] bye-bye.
– “Tabee”: so long.
(Semi-)formal
– “Tot ziens”: goodbye.
– “Tot horens”: [on the phone] bye (lit.: until we hear each other again).
– “Dag”: bye.
– “Tot de volgende keer”: until next time.
– “Tot snel”: see you soon (lit.: till soon).
– “Tot binnenkort”: see you shortly (lit.: till shortly).
– “Vaarwel”: farewell.
