Cleaning Kitchen Cabinets Left Streaks?

I have wood cabinets with a sage green veneer. I am redoing my kitchen and wanted to really scrub the cabinets of all residue. I used a Magic Eraser and hot water and scrubbed, then wiped with warm towel. My cabinets are clean, however, they are streaked and have a white like film. Any suggestions? And then what do I use to re-luster them (polish)?

By dawn