Don't strain! You'll oxidize the cider by pouring it through cheesecloth or a strainer. Use a racking cane and some tubing, and siphon to the new sanitized container, leaving all of the lees (the sediment on the bottom) behind. Rack only when the cider is clearing or clear, and that will leave far more sediment behind.
I posted a picture of my latest cider, at the beginning, and then on racking day (about 5 days later):
You can certainly add more fermentables to boost the alcohol %., but keep in mind that you have to know where you started as you do not want to go over the alcohol tolerance of your yeast strain if you want to carbonate it later. Also, you need a hydrometer to know when your cider is finished.