Hi M..
My sons are 20 & 18. I have been through something like this before, with the both of them. When my boys lied to me (and I would always give them 'the look' that they knew meant I knew they were lying), I would tell them that telling me the truth first is always better, they came around (eventually) out with the truth. When they kept lying to me, I would take things away from them (phone, computer, video game system, stereo, MP3 player, hanging with friends, etc.) - anything fun or needed.
As for the hygiene, I used to tell my boys that they don't live in a nursing home so they can and WILL wash themselves daily. I also added in that girls tend to be attracted to guys who take care of themselves WITHOUT being told to. I know it sounds easier said than done, but if you keep repeating it, the message will eventually get through.
I really don't know what to tell you about how to handle the situation involving the father's girlfriend. One would figure that after 10 years of them being together, your son would have been used to it by now. You son's probably feeling like he can't really talk with his dad; like the father's girlfriend is putting in her 2 cents when its just supposed to be about the father and son. Maybe you can talk with your son's father (when your son's not around) and try to get some sense into him about the father/son relationship.
Learn the lyrics to the songs your son listens to, also. Even today, there are questionable lyrics in songs that are considered 'underground.' My middle son once had me listen to songs in which the lyrics stated that 'cut yourself cuz it makes you feel better.' <- Songs with words like that just seem to feed the depressive/suicidal ideation. If after everything, your son still seems to be in the rut he's in now, you may want to consider both individual & family counseling sessions for your son.
I know there are days when you just want to put your hands on your son's shoulders and just shake him - hoping to snap him out of whatever's going on inside of him - but deep down inside, you know it won't work. Just keep at it and follow the advice of others that have been there. You may want to even consult his physician. Physician's can provide advice and help when all other avenues have failed.