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No. Doing so just makes a natural mix of HOD, D2O and H2O. The hydrogen-oxygen bonds aren't quite as static as chemistry class makes them sound.

HDO molecules do exist, the pure substance does not. Some of it always disproportionates into H2O and D2O. It's not like the substance would have any uses though, it's just an intermediate in the isolation of D2O.

Oxygen bound positronium would result in the state that is depicted on the right I reckon; not too stable to say the least but certainly quite a bit lighter than ordinary water. 👨‍🔬

Wait. Is heavy water hydrogen with a neutron, regular water is just hydrogen, and light water is...well...a very lonely electron?

Well heavy water is D2O. Semiheavy is DOH. So if he really meant the first one as heavy, then the last must be positronium oxide or muonium oxide.

Positronium is an electron orbiting a positron (antimatter version of an electron). Muonium is the same thing, but with an antimatter muon (somewhat similar to an electron, but heavier). Both are extremely unstable.

Yes, positronium compounds have been made. Positronium has a half-life of 0.12 nanoseconds while molecule formation happens on the order of attoseconds once the component atoms are in direct proximity. It's very, very fast.