Q:

How can one fight an unfair/corrupt employer/union (working hand in hand)?

EDIT:
My original title focused on the union, but I changed it to include the employer. They're both working hand in hand against the interests of the employees/dues-paying union members.

Imagine a Corporation (C) that's affiliated with a union (U). They agree on a contract that says extra work should go to more senior people. If the company needs to call people to work an extra shift, it is supposed to call the most senior people first.
However, the company blatantly ignores the contract, recruiting the LEAST senior people.
When an employee with seniority with high seniority files a grievance, C and U both lie, intimidate and stonewall. For example, the union claims the company won't give them its payroll records, making it impossible for them to know who worked when. And when the company finally hands the records over - three months later - the union won't let the grievance see the records.
The union also makes grievance jump through all kinds of hoops. If you file a grievance, you're expected to do all the detective work - cite a particular less senior worker, with details (time, date, location) and have it signed by a witness. The irony is that there could be a dozen less senior people who worked that day, a fact the payroll records could easily prove.
But the union refuses to go on a "fishing expedition."
Long story short, grievances are typically solved six to nine months after they're filed, and the grievants never expect to get more than about 30% of what they're owed.
The state Dept. of Labor says "contact the National Labor Board." The National Labor Board says a contract - and its interpretation - is between C and U; they can do whatever they want.
Is that really the end of the road, or is there some kind of legal or quasi-legal action one could take? If you know the company and union are both withholding information, lying, delaying payouts, etc., can you cite them for violating any particular laws? What about a union that "interprets" and enforces the contract two different ways, giving its cronies all their support while thumbing their nose at everyone else?
It appears that the only recourse would be legal action, but it's hard to determine whether any laws have been violated. Moreover, the employee can't afford to hire an attorney. Would this be case that the ACLU or some other organization might help with?

A:

...is there some kind of legal or quasi-legal action one could take?... Would this be case that the ACLU or some other organization
  might help with?

Try writing a detailed letter with documentation to the state attorney general's office. (And include the fact that you talked to the state Dept. of Labor and the National Labor Relations Board).
The state AG has a lot of power and would be interested in possible conflicts and corruption at the corporate and union levels.
You don't need a lawyer to write the letter, but make it as clear as possible, and base it on facts, not emotion. It sounds like you have enough documentation to show the AG that you have a possible case.
Whether to take a look into the case will be the AG's discretion. But the AG will know how to deal with the NRLB, the union and the corporation, and will know if there are possible conflicts of interest in the contracts, the grievance process and the decisions, and the possibilities of corruption. 
If the AG gets interested, a simple phone call or letter from the AG advising the union and the corporation that the state might be interested in the situation might magically make a difference.
You could talk to the ACLU, but their mission is a bit different than labor relations; they might suggest another organization. You could Google for free legal aid in your area - the state bar may provide help, or one or more non-profits - to see if their office might help you compile the letter and documentation to the AG. Free legal aid organizations may not want to say they will represent you right away, and many times they have limits on what they can get involved in (i.e., only civil cases and not criminal cases), but it's worth a try.
Another option is journalism; try getting a local paper (one that is more than a weekly; a daily paper with good circulation) interested. If you can get a reporter involved, they will look at the evidence and documents and know if there is a story, and they will know enough to not libel anyone if the story is speculative in nature (and the paper will have their own lawyers to protect themselves). To be honest, whether the paper runs the story may depend on the publisher's political leanings and the business office of the paper, but it's worth a try. A good news story might magically make the union and corporate boards more interested in being better citizens and might in fact uncover possible illegal acts, and that would help get the local county attorney or AG interested.
You could always blog about the situation and your investigation on your own website, but you would need to be extremely careful not to libel anyone.

