As far as I can tell, wards affected by a red trinket behave as if everything around them was in a brush. So you lose all vision normally, but just like if a champ attacks you from inside a brush, the champion is revealed if they attack the ward.
Invisible traps will behave differently depending on how they were revealed. If they are hit by the sweeper directly (have the stunned icon above them) then they will not activate until the effect expires*. However, if you reveal the trap with the Oracles portion of the Oracles lense, it will be visible, but still active, and can be triggered.
*Note: this is very handy when fighting Teemo and Shaco. Often times these champs will lay down a shroom/box before or during combat and try to lure you onto the trap while you are fighting them. If you use the red trinket, it disables the trap and you can ignor it and keep attacking Teemo/Shaco. (While the effect lasts, of course.) Note that you have to disable Shaco boxes BEFORE they trigger, once they start attacking (and fear you) a red trinket will have no effect on them.