How to fight tons of unresolved variables warning in WebStorm?

Use JSDoc:

/**
 * @param {{some_unres_var:string}} data
 */
function getData(data){
    console.log(data.some_unres_var);
}

JSDoc the object. Then its members.

/**
 * @param data          Information about the object.
 * @param data.member   Information about the object's members.
 */
function getData(data){
    console.log(data.member);
}

• @property for local variables (non parameters).
• Tested in PyCharm. @Nicholi confirms it works in WebStorm.
• The {{ member:type }} syntax Andreas suggested may conflict with Django templates.
• Thanks to Jonny Buchanan's answer citing the @param wiki.

To document arrays of objects, use [] brackets as JSDoc suggests:

/**
 * @param data
 * @param data.array_member[].foo
 */