Quickest way to cure fungus infected toe nails?

No quick way. There is no quick way. Because of the slow rate of nail growth most treatments take up to a year whether topical or oral medication.
Laser. Yag laser can have the quickest effect but there is no proof the results will last more than 1-2 years. The usual treatment is oral Lamisil (terbinafine) for 3 months with the effect occurring over one year.