Try squirting a large bottle of "tough on grease liquid dish soap" on the tile. Spread it around with a cleaning brush and let it sit for 3-4 hours. It will dry a little, but that's O.K.
Then, scrub the tile with a no scratch brush. That should do the trick.
For cleaning the grout add mixture of 3/4 white vinegar and warm water and scrub it down. That should do the trick.
Once you have cleaned your tiles, and if no other product was used previously, you can reseal your ceramic tiles with a high or low gloss sealer. Many companies make this sealer. I have used the Aqua Mix brand name and it works very well. It can be used for natural stone, porous tile and on the grout. For the high gloss sealer, the more coats you put on, the higher the gloss. The expected wear is 3 years. Let me know how that goes! - Evette