I read the related post, but my situation is a bit different. Additional background - I installed new 105 shifters and derailleurs two years ago (~5000 miles) along with chain and cassette. I also had a 53T chain ring put on in 2013. All was good. Had slight hang-up with slack shifting (to higher gears) on rear cogs this spring, so I replaced the cable and sheaths to the rear derailleur. All was good again. The bearings in my freewheel started making noise last week. Which brings me to the present.
I just replaced the rear wheel, cassette and chain on my 30-speed road bike. The derailleurs shift perfectly and the chain travel when pedalling is smooth and quiet. However when I stand up or dig in on a hill the chain will skip on the cassette. It happens on all THREE chain rings in the front and the spectrum of cogs on the cassette. I thought sure it was a stiff link in the chain, but could not find an issue with it when manually flexing each link. I tweaked the rear derailleur to the point of shifting cogs in both directions and still have the issue. Any suggestions?