I need to patch these holes in the subfloor where the vents are. These holes are from a return vent that is being moved, the joist cavity below these holes is a return duct. I'm assuming using blocking would affect the airflow. Is it acceptable to patch the subfloor right in the middle of a joist where you would have 3/4" of the patch on the joist and 3/4" of the existing subfloor on the other half of the joist. Or should I use a larger patch and go past the joist and use blocking. Do the other two sides of the patch need to be supported. The subfloor is 3/4" plywood and the joists are 16" OC. The slate floor and laminate floor in the picture have been removed and the finished floor will be either hardwood or an engineered floor. How do I patch this and not affect the airflow in the return vent. 
How to patch a subfloor over a return duct cavity
carpentryductsfloor
Related Solutions
Duct Tape is good for a lot of things, except duct work! It will eventually dry up and pull away from the heat in the vent.
I would bend/dent one of the ends slightly so that it will fit easily inside of the other. Then I'd secure it with proper HVAC foil tape, followed by a clamp around it.
Foil Tape
(source: homedepot.ca)
Metal Gear Clamp
(source: homedepot.ca)
Not doable at all.
Old houses have 3/4'' thick wood planks as subfloor, not 8x4 sheets of plywood like today's houses, so I would say that it's ok to consider your hardwood floor the subfloor. That's if you're putting another wood floor on top.
However, for the purpose of tiling you need an additional layer of plywood to reduce deflection that will cause the grout to crack eventually. And on top of that you would install your cement board. The cement board itself provides no structural support and is only used as a decoupling between a wood subfloor and the tiles, so the lateral movement of the wood is not going to cause the tiles to pull up. You can always use a durock membrane to reduce thickness, but you still need a floor that will not deflect.
If you really want to do this right you would take out the old floor down to the joist and install some OSB and then do what you want...
Best Answer
"The slate floor and laminate floor in the picture have been removed" - well that takes all the fun out of it.
Cut the sub-floor down the middle and right green lines. Remove. Replace. Otherwise you'd of had to cut the tile in-situ down the middle green line; that'd be the fun part.