How do I rid mildew on oak wood?

a pic?

lye

1) Find and seal the water leak. Or use a proper vapour barrier to prevent condensation.
2) Wash the mould off with a 5% bleach and water solution.
3) Use a dehumidifier to lower the water content in the wood.
4) Refinish the surfaces damaged by mould.

Use a respirator while cleaning up the mould. Many moulds are a respiratory irritant and can cause lung damaging pneumonia.

Personally I would hire a specialist that knows what to do and provides a warranty on their work.