How can I quickly cure calusses and corns?

Several ways. Having them flied or trimmed by podiatrist will relieve symptoms. Determining cause and eliminating this will help to prevent problem from constantly recurring. Change of shoes, orthotics, paddings or surgical correction of deformity are ways that may address these causes.
Trim them. With an emory oard or electric file, or visit a foot doctor.
Rid of corns... See a podiatrist to trim them, custom orthotics would likely help and last resort is surgery if all conservative treatment fails.