Read up on categorical variables, dummy and dichotomous variables in multiple regression as search terms. If all variables are categorical, you are really doing the same thing as ANOVA.
You need to leave out one variable as the reference variable, not sure from your description if you are doing that. I.e. You can't have two columns that are the exact opposite, let's say you sold tables and chairs, and you entered in a column where 1 = chair, 0 = not chair, you would leave out the column where, 1= table and 0 = not table. Some software will drop it one automatically, some will just return an error, but sounds like you are doing custom work.
If you are using a dichotomous 0, 1 variable as a dependent variable, use binary logistic regression and interpret using the odds-ratios.
http://groups.chass.utoronto.ca/pol242/Labs/LM-9B/LM-9B_content.htm
ETA: by reference variable, let's take race as an example, four options, you would enter in three columns of 0/1 dichotomized (dummy coded) columns the one you leave out is the reference, and you compare the coefficients as +/- in relation to that one you left out. Leave them all in, and you get multi-collinearity. Doesn't matter which one you leave out, that only changes your intepretation.