I believe that the only items that fit the aforementioned criteria are Key Items. All Key Items in ORAS are as follows:
>Acro Bike/Mach Bike
Aqua Suit/Magma Suit
Clear Bell/Tidal Bell
Devon Parts/Scope/Scuba Gear
Old Rod/Good Rod/Great Rod
Intriguing Stone (before it is made into the Pidgeotite)
Meteorite (until Rayquaza eats it)
Oval Charm/Shiny Charm
There are also several items that are only Key Items for a limited time, such as the Scanner, Letter, and Sea Mauville Room Keys. For a complete list of Key Items, look here.
You can also not sell any TMs, HMs, Mega Stones, or Master Balls. Note that Master Balls can be 'Trashed', so they sort of count as unreleaseable.