Pay attention to where your wireless gear is located. Cellphone, WiFi router, iPad, cordless phone etc. all make interference in the lab. Before you blame your equipment.
You can try clamp-on ferrite beads or move the leads or equipment, add a small disc cap across the input jack, to see if that changes the birdies. Chirps, whistles I get from my PC speakers if my cellphone is downloading a text message, and there is the regular packet heartbeat as well. Very hard to filter out.
I find oxidation on cheap chinesium plated probes creates all kinds of poor connections, rectification, half-cell potentials - totally unsuitable for low signal work. It seems to be some chromium, steel mix at the tips and banana jacks. Terrible plating.
If you leave the laboratory and use a multimeter out in the wild where there is dirt, moisture, corrosion - the high input resistance is no good and you will get ghost readings. This is why LowZ voltage functions are very useful and a basic need when troubleshooting.