To unlock the Strange Things are Afoot trophy in Red Dead Redemption you need to complete a task for a Stranger. Strangers are the question marks on the map that only appear when you travel nearby, and their quests are indeed often strange.
An early one you will come across is down on the zig-zagging decline between the McFarlane Ranch and Armadillo, a road you will travel plenty of times in the game's opening story missions. At some point a man should appear at a camp before you reach the foot of the cliff and head towards Armadillo. Sit with him and he will ask you to get a deed off of a gentleman by whatever means you see fit. Head to the purple marker that appears on the map, deal with the man either violently or otherwise and return the deed to the Stranger. As soon as you complete the task the Strange Things are Afoot trophy will unlock.