I'm replacing a section of 4'' load bearing wall by a large 8''x8'' steel beam, and due to the size of the beam it would stick out to one side too much if I were to install it exactly centered with the current wall. I would need to offset it by about 3 inches to keep one side of the beam flush with the remaining section of wall. The joists above are lapped. Is this possible or the beam has to be absolutely centered with the existing wall?
You've essentially got a column buckling problem here. Factors affecting the maximum load include the geometry of the beam cross section, its material properties, and the manner which its ends are constrained. You can read up on it here.
What makes it more complicated is a possible eccentric loading condition, as The Evil Greebo points out. Now you have to worry about compressive stress and normal stress. This eBook does a good job describing the loading conditions and resulting stress under the "Maximum Stress" section.
Since the current exact loading conditions are unknown, and in addition you're changing the location the load is applied in, I think it would seek professional engineering advice. (I would, and I'm a mechanical engineer - I just don't specialize in architecture.) Either that, or an experienced contractor may be able to give you a better answer. (Shirlock, where are you on this one, buddy?)