The first thing I would suggest, as a homeowner, is to take a few photos of the items you've described - digital is ok, polaroid is good for immediate results and follow with a regular camera so there's a set of paper copies, too. Do it safely and by all means, keep yourself, your children and your pets away from the problem areas. I would also be interested in whether this is a home you own or are renting. If renting, the landlord may need to or be required to bear some of the cost of repairs. If public housing, yet another layer of responsibility lies with the housing authority. You will find the photos will serve you well in documenting existing conditions.
Second, call a local inspector - asap. Have the inspector give you the information on what the code is and the violations or potential problems.
Third, have your utility company inspect and correct any problems that are within their area of responsibility (outside/entering the property and/or connecting to the service panel).
Finally, get a reputable electrician to come correct any remaining problems. Show him the photos, have him look at the inspector's report and make sure you have an assurance or guarantee of safe conditions before he leaves.
It may cost you some out of pocket expense, which not everyone has extra money for, but the cost of NOT doing something about it might be the loss of a life or an injury. If you need financial assistance, contact the utility company or a local church, but please don't let 'live' electricity go unchecked in your home.