The song is about the execution of a martyr and the different possible viewpoints of the event.
I think the most important part is how each verse describes the same event but from a different perspective.
First Verse (An unbiased description of the event):
Are you, are you
Coming to the tree?
They strung up a man
They say who murdered three.
Strange things did happen here
No stranger would it be
If we met at midnight
In the hanging tree.
Second Verse(How the Capital wants you to view the execution.):
Are you, are you
Coming to the tree?
Where dead man called out
For his love to flee.
Strange things did happen here
No stranger would it be
If we met at midnight
In the hanging tree.
Third Verse(How the rebellion views the execution):
Are you, are you
Coming to the tree?
Where I told you to run,
So we'd both be free.
Strange things did happen here
No stranger would it be
If we met at midnight
In the hanging tree.
The first verse is a simple unbiased description. Note the "They say" there's no biasing about whether the man was guilty or justified. Just that the authority claims he was a criminal.
The tree is the rebellion. The "Strange things" are what happens when you rebel. It's an unknown. Noone knows what will happen if a rebellion were to take off. Meeting in the tree at midnight is joining the rebellion.
The second verse is how the Capital hopes you'll view the execution. They're killing this man as a warning. In this context:
Are you, are you
Coming to the tree?
Is a threat. Are you joining the rebellion? Well look what happens.
Where dead man called out
For his love to flee.
This man's death is a warning to flee to safety. Keep your head down and do your job. Prize your safety over your freedom.
The "Strange things" that happen at the tree if you come is the scary unknown. If you rebel, then bad things happen. You'll die, your district will be razed, disorder and chaos. Your life might be bad, but at least you're familiar with it. If you rebel, then who knows what will happen? But it will probably be bad.
The third verse is only slightly changed, but it turns everything on it's head.
Are you, are you
Coming to the tree?
Where I told you to run,
So we'd both be free.
This is a call to arms now, not a threat. The martyr is not calling you to flee to safety. Notice how "Where I told you to run" follows mentioning the tree. He's calling you to run to the tree, not to flee to safety like Capital's intent. In this context, the "Strange Things" reference a successful rebellion. The idea that the districts could be free is strange and unknown. Where the Capital wants you to be afraid of the results of a rebellion, the martyr wants to spread hope that the rebellion can be successful.
The final verse is the rebellion calling you to stand "Side by Side" with the martyr and fight for your freedom.
Are you, are you
Coming to the tree?
[Movie line:] Wear a necklace of rope,
[Soundtrack line:] Wear a necklace of hope,
Side by side with me.
Strange things did happen here
No stranger would it be
If we met at midnight
In the hanging tree.