Take a look at this,
It plugs into or pairs via BlueTooth to an Android phone. It has the IO pins you need to talk to your sensors and it can talk to the phone. If you must use the Arduino you could use the serial communication on this board to do that.
As for just plugging an Arduino into a phone, that won't work because they are both perifierals and neither is a host. Their are host shields for the Arduino, but things can get complicated going that route.
If you don't need to exchange much data you might try making a visual link. By toggling the flash LED on and off and watching it with a photodiode connected to the arduino you could likely estabolish some rudimentary communication. If your app can output audio you might also be able to make a link via the headphone port and an analog input on the Arduino. I hope these ideas give you somplace to go. Feel free to ask for more info on any of them. I can't say I have ever tried this, but I am happy to throw out suggestions.