First off I would get rid of all the old plates and order some new ones so you can start making solid growth medium from scratch. Autoclaving any medium, which is required to dissolve agar should definitely take care of any transient contamination that may be in some of your reagents. If you want to go all out, order new reagents for the medium you're making as well.
In our lab, we work with super persistent spore-forming bacteria which bring their own set of problems. Typically a more diligent sterile technique is usually sufficient to get rid of everything. We use 70% ethanol to wipe down all surfaces and work by a flame, and in some cases we use 10% bleach and UV light to sterilize as well. The latter approach has worked very well even when working with extremely sensitive material such as Arctic sediment where contamination becomes fairly obvious once you run it for sequencing.
Other than a more diligent sterile technique, I suspect maybe you have issues in your culturing vessels as well? Again, bleaching and rinsing very well with distilled water should be sufficient if you can't get your hands on an autoclave, which is the ideal version (you don't want to autoclave something with residual bleach, it will make chlorine gas). When I worked with Euglena gracilis, I didn't have issues with contamination because it can grow at extremely acidic pH ~3.5 however, when we did transfer it to a pH 7 medium we took some precautions. First off, we autoclaved our foam stoppers and generally only used them once. Any lines we used for bubbling we either 70% ethanol rinsed and UV sterilized or moved to stainless steel needles that could be autoclaved and easily manipulated. Finally, we also used what I call a fancy napkin, it's a product called bio-shield and it has 0.2 um sized pores on it that can be autoclaved as well. Assembling all of this in a biosafety cabinet allowed us to maintain axenic cultures over months with no observable contamination.
I know many of these tips are about keeping cultures pure, but they can essentially be reversed engineered to keep your lab Chlorella-free and to prevent another widespread contamination. Unfortunately, it sounds like you may have to team up with some lab mates for a good old fashion spring cleaning. I hope that this helps!
I am not familiar with the use of an ozone generator, but again that seems like a very expensive solution that could be avoided. We have used the sterilization steps I mentioned in my previous answer to rid the lab of spore-forming heat resistant bacteria, and if it works for that it should work for algae. Other than that, if it an issue with contaminating human cells lines I have had colleagues try to eliminate fungal contamination and it basically requires taking incubators apart and cleaning everything piece by piece, or, simply getting new incubators unfortunately. I hope this is not the case for you but please let me know how it turns out!