Creak (“To make a prolonged sharp grating or squeaking sound, as by the friction of hard substances”) is the most-commonly-applicable term for sounds made by parts of trees moving in the wind rubbing together. An answer to Question380662 at theanswerbank.co.uk explains fairly well one of the sources of creaking:
... when the wind blows, and its force moves the tree, the tree does not move uniformly.
As a living organism, a tree is in a constant state of development, so the fibres in its trunk and branches are all at different stages of development - some are fully mature and dry, some are new and full of sap. As the trunk and branches move, different areas of the wood respond differently. Some move a good deal, some don't move at all.
As different fibres with different tensile strengths which are in close proximity react - or not - to the force of the wind, they rub against each other with friction. This is what causes the distinctive 'creaking' noise when a tree is bending in the wind.
Another common source of creaking is that different large limbs of a tree may curve and cross each other, thus making creaking noises as the wind moves the limbs independently.
Crack, crackle, groan, and boom are other verbs commonly used to describe tree sounds. Cracking and crackling often occur during cold snaps that freeze some of the tree's sap. Boom is used several times in a New York Times article about New Yorkers injured by trees or limbs falling on them. The article incidentally mentions some of the noises that occurred before the incidents; for example:
Mrs. Berger’s was among at least 10 lawsuits in recent years that have raised questions about whether more diligent tree care by the city might have prevented the crack — or creak or boom — and the death or injury that it brought.