As a US citizen, you should not have too many issues to renew your visa for another 6 months. You should have done that at the embassy before it expired though.

I don't think there is much chance the immigration agency will go straight after you at your friends' house (they have much more on their plate). However it may cause trouble if you need to show your passport for some reason.

 

In theory you need a visa.
However you might get away with it once by making a small trip (a day or more) to another EU country, and then enter the UK again to get your passport stamped and get another 6 months.
However I strongly advise you to get a visa if you really intend to stay longer.