At the end of the third Hobbit movie, I recall Thranduil telling Legolas to go north to look for Aragorn. They were at Erebor, and north of that was just the Iron Hills and Forodwaith. Aragorn would not be north of the Wood-elven Kingdom either. What did he mean? Am I misunderstanding the scene?
This scene and dialog was invented for the movies and doesn't occur at all in the books.
You're correct that it's difficult to reconcile with the geography of the books, and difficult to determine exactly what Thranduil may have meant.
The only reasonable explanation may be that Aragorn was at that time ranging north of Erebor, and Thranduil knew it. Since the movies operate on a different timeline to the books, Aragorn's age of 10 in the books would be irrelevant and this is possible.
Perhaps when the extended edition of Battle of Five Armies is released, the director's commentary (or some extra scenes) may reveal more. Until then all we can say is that we don't know what was intended.
I think that Legolas was told to meet the young ranger, Aragorn, and then return to Woodland Realm. Then few years later Aragorn captured the creature, Gollum and brought him to the Mirkwood as a prisoner. Then Aragorn returned back to North. After Gollum escaped from Mirkwood, Legolas came to Rivendell to inform about it to Lord Elrond. So then he accidentally participated the council there and became one of the Fellowship of the Ring.
Actually, I do believe the answer CAN be found in the book.
Specifically, in Appendix A of The Return of the King, it is said that:
... cut for brevity with relevant information being that Elrond confronts Aragorn about his heritage and hinting at how Arwen will be affected ...
'After a few years, Gilraen took leave of Elrond and returned to her own people in Eriador, and lived alone; and she seldom saw her son again, for he spent many years in far countries. But on a time, when Aragorn had returned to the North, he came to her...
... cut for brevity with the only other relevant mention of time being related to Gilraen's passing before the spring that followed ...
'Thus the years went on to the War of the Ring; of which more is told elsewhere...'
According to the timeline in Appendix B, this incident would likely coincide 10 plus years later in 2951 after the Battle of the Five Armies and after Elrond has disclosed to Aragorn the truth to his heritage.
That said, though the dates aren't completely matching, Thranduil's instructions for Legolas to go North - while perhaps a bit premature - makes sense...
while also hinting to the fact that it will be Aragorn who will find and capture Gollum and bring him to Mirkwood in another 60 or so years in 3017 and whose subsequent escape will be what prompts Legolas as a representative of Mirkwood and Thranduil to seek counsel from Elrond in The Fellowship of the Ring.
Legolas also said he rides north to Gundbald after Taurial is banished, so it could be they just don't know which way North is. Legolas was also backwards on his directions in the Two Towers on wich way the Orch were heading with Merry and Pippin.
Strider and rangers are from the north. So when Thranduil said go to the north he somehow meant he will go and live with the rangers. Thranduil also said go to the Dunedain which by what he said is probably on the north.
I felt like what he said about a Ranger ment the Game Shadow Of Mordor. The main character dies in battle and becomes one with the creator the rings. I think I've heard him been called strider and all. Shadow of Mordor happens Between Hobbit and the LOTR. I never got to play the game so I don't absolutely know if this is accurate but it's my best Guess. SOM takes place in The Orc strongholds and they do refer to the Orc strong holds as to the North.