It depends on the kind of movement. Of the three you mention, I would pick "sway," because that suggests a slow, graceful, stately movement. Branches "sway." "Swing" is another possibility. "Wiggle" and "jiggle" suggest rapid, irregular, undignified, almost comical movements. Smaller parts of the tree might "wiggle" and "jiggle." The Quaking Aspen is a tree common in North America, in which the leaves have very flexible stems. For this tree, one might say "The boughs swayed in the wind, while the leaves danced, shimmered, and jiggled." (Or fluttered, shimmered, shook--and quaked). This is the kind of question that sends native speakers to the thesaurus (a reference book that lists synonyms). Since you are trying to be poetic, you have many words to choose from. Since you are comparing boughs to arms, you might use words that apply to arms; the first one that comes to mind is "wave." A rather pretty word is "undulate;" it expresses passive movement, so you would say "the trees are standing naked, their arms undulating mournfully." "Naked" and "nude" carry a slight erotic overtone; you could make that a little stronger by using words that are used to describe the movements of dancers, such as "shimmy," "wriggle," and "writhe." Or, you could suggest fear or discomfort with "shivered," "shook," and "trembled."

Sway is very common for slow moving trees and branches in the US as well. Wiggle and Jiggle tend to describe quicker movements. Shivering would be common for tree limbs in the winter here as well. Once you're writing poetry there can be a conscious reason to choose uncommon usage. I think trees are more often described as bare or naked than nude, but I can't really think why naked is more used than nude.

In UK English it is most common to describe trees as swaying in the wind. Sway/swaying/swayed. Poetry is very different to prose though and often you would use a very different word than normal everyday speech. For example, you could say the trees 'shivered' in the cold if you wanted to portray a sense of movement and winter.