A poop-noddy is defined in the Oxford English Dictionary as:
Sexual intercourse (rare)
I don't know about you, dear reader, but I'm planning never to have sex again, it's pure poop-noddies from here on in. However, the origin of the word is rather curious. The OED refers you to noddypoop and noddypoop is simply a synonym for noddypoll.
Now a noddy is a fool and a poll is a head. That's why you have poll tax (a tax per head) poleaxe (an axe used for chopping heads) and tadpole (toad-head). So what has any of this got to do with sex?
Well, there's a sort of clue in Shakespeare's Pericles. There's a scene where two people who run a brothel are discussing how drab and diseased their prostitutes are:
Pandar: Thou sayest true; they're too unwholesome, o' conscience. The poor Transylvanian is dead, that lay with the little baggage.
BOULT: Ay, she quickly pooped him; she made him roast-meat for worms. But I'll go search the market.
You've definitely got a sexual context here, but poop seems to mean gave him syphilis, rather than sex. So I'm going to take a guess that poop-noddy isn't sex exactly, that it is, in fact, the act of cuckolding somebody. So if you have sex with somebody's wife you are pooping her noddy of a husband.
I could be wrong though. It could be to do with poop decks, which are owned by bad DJs.
Supply your own caption.
P.S. Why do elephants have big ears?
Because Noddy won't pay the ransom.