All the vents you propose are illegal. Code prohibits any horizontal run of a vent until the vent line reaches an elevation at least 6" higher than the flood level rim of the highest fixture served by that vent. If you can make a drawing of your floor plan and email it to me I will work out your layout, then we can post the illustration for others to see.

Pressure fittings are defined by the angle of the change in direction they make. I.E. a 90 deg elbow, 45deg elbow, 60deeg elbow etc. In order to help insure we don't mix them, DWV(drain,wste & vent) fittings are defined by the fraction of a circle the change in direction makes. A full circle is 360 degree so a DWV 90 deg elbow would be 360/90 = 4 or properly its called a 1/4 bend. 60deg = 1/6 bend - 45deg = 1/8 bend. A common fitting has a female hub on each end but a "Street fitting" has a female hub on one end and a male raw pipe size on the other end. To make the offset you would begin with a Street 1/8bend with the male pipe end directly into the TEE of the waste & overflow. This would change the direction to 45 degress. Install a length of PVC in the female hub of the 1/8 bend and run the offset down at 45deg to the point where your trap will be. On the bottom end of the 45 deg offset pipe you install another street 1/8 bend with the pipe into the female hub, This will change the direction from 45deg slant to vertically down and it would leave a raw male pipe end that will fit directly into the input of the P-trap. You will find the fittings in both ABS and PVC at any local hardware or home supply store. The choice of which material to use is determined by what kind of pipe you have now. Code prohibits glueing dissimilar plastic so if you have ABS you would use ABS, if you have PVC you would use PVC. In this case you have cast iron so you may use either material as long as all the pieces are the same material.

Thanks for the help, a quick follow-up: The toilet waste line is vented by a 3" line that extends upward. The wye for the tub drain will be between the toilet trap and this vent line for the toilet. So, this vent which would be about 4' from the tub trap could also serve as the tub drain vent. Here is a sketch that may clarify: http://picasaweb.google.com/cjtully/Bathroom#5263299906822545778 The sketch shows a proposed new vent that I can't really run unless it is on the horizontal till it hits the wall. So my hope is that I can wye of the 3" toilet line and also share its vent to add the new tub drain location.

I believe the distance allowed between a plumbing fixture trap and the vertical vent piping depends on the diameter of the drain line not what you stated which is if you drain into a larger diamter pipe no vent is needed. That being said, I think in your case, since you have 1.5 inch on the laundry tub, the trap arm(pipe between the trap weir and the vent pipe) should not be longer than 3.5 feet(42 inches)before it reached the vent line. Double check with your city plumbing inspector and pose the question to him/her