Need some help getting started: cardio and strength training (a little long, but relevant info provided)

Hi loseit! I'm getting sick of feeling like crap and I'm just starting a workout routine. I was wondering if I could get some pointers specific to my situation.

Stats: 24/F, 145 lbs, 5'5"

Living situation: I live at home to save money while I'm finishing up school. As a result, it's not economically feasible to simply buy my own food. I can request certain things on the grocery order for my lunches, but I eat supper with my family. I have to explain that my stepmother is the diet-sabotaging type. Dad goes on a diet - she switches from skim milk to 2%, knowing he drinks a ton of it. With a little pressure, she does cook healthier for a little while, but switches back to her regular recipes (most of which contain a ton of cheese).

Equipment available to me: Thanks to a jackhouse brother, I have access to a treadmill, a resistance band, a yoga mat, several different weights, a weight bench and a pull-up bar.

Dietary progress so far: I used to eat at night, drink soda, eat out often and eat from the campus cafeteria. Now I don't eat at night or drink soda, I eat mostly at home and I eat smaller portions. However, home probably isn't as healthy as it could be.

Vices: I have bad sleeping habits thanks to 6 years in university over 2 degrees (habitually 5 hrs a night during the week) and I mostly crave salty things (which I'm told makes you retain water horribly). On the plus side, I don't mind water and I can easily switch out all drinks for water or green tea.

My weight fluctuates several pounds from day to day and my weight is going in a downward trend, but it seems like I'm not moving much. I've been doing 500 cal walking/jogging sessions on the treadmill 3x/week and a friend suggested I start doing strength training so that I don't look like a bag of milk when the fat does come off. I don't really know what I should be doing in the strength training department and need a little help getting started. Any pointers would be welcome - for workout or for diet.