re: OT Electrician advice needed: running 110v off of 220v line

Is the breaker for the existing oven either 15A or 20A? If not, then you definitely can't do it without adding a load center to split up the loads.

Without digging into code to see if this is even allowed: if the existing circuit to the oven has a neutral, then you could theoretically add the additional receptacle across one of the lines + neutral. The receptacle can be GFI type (only 120V, 15/20A receptacles in kitchens are required to be GFI, the 240V isn't). The problem is that if you plug in anything of consequence into that receptacle (microwave, blender, coffee maker, etc) then the breaker is liable to trip while that device and the oven are on at the same time. This is especially true if the oven has been on for an extended period of time. This is still an issue if you add a load center to split the 240V circuit into the 240V + 120V circuits.

While it may be more time consuming, you'd be much better off just extending a nearby 20A, 120V circuit serving a nearby receptacle.