So I read this article and some of the numbers claimed by Greek and Roman weightlifters seems absolutely unbelievable, because they rival or even exceed modern day world records in similar lifts. For example:
Anther famous ancient Greek weight lifter was Bybon (early 6th century BC). A block of red sandstone weighing 143.5 kg (315 pounds) was found at Olympia (on display at the Archaeological Museum of Olympia), with the carved inscription, “Bybon son of Phola, has lifted me over his head with one hand.” The stone has a section carved out as a hand grip.
The nearest modern equivalent to this would be the push press, and although there is no record for this movement, various internet sources claim unofficially around 450 pounds. The world record clean and jerk (for which records are kept) is 266 kg, and while this is a decent proxy for lifting a stone above your head (since the latter part of the movement is just that), it is not a perfect approximation because of the clean part of the movement. But both of these movements are with both hands. Further, modern day weightlifters profit from state of the art facilities, nutrition, coaching; they lift from when they are teenagers (for most Olympic weight lifters) and also benefit from steroid usage. And yet this guy was lifting near those numbers with just one hand.
Perhaps an even better approximant to that movement is the one handed kettlebell jerk, since both movements involve a round thing with a grip (the stone Bybon used has a grip carved into it). But the record for that is a "measly" 90 kg.
Further consider:
The stone has a section carved out as a hand grip. Another stone, found on the island of Santorini (Thera), weighs 480 kilograms (nearly 1060 pounds), also dates to the 6th century BC and has the inscription, “Eumastas, the son of Critobulus, lifted me from the ground.”
A good equivalent is the deadlift. A new (raw, meaning no equipment) world record was just established at 461.983829 kg (1,018.50000 lb)
Yet some random dude from the 6th century BC beat that without any of the benefits modern weightlifters/powerlifters enjoy? Without even a proper place to grip, which a barbell offers but a lunky stone does not? In modern times, the world deadlift record was "only" 725.75 pounds as late as 1949. In modern times, it wasn't until 2006 that the 1000 pound mark was passed.
What gives? Were the ancients fibbing? Or were they really that strong, in which case, is it just that we are weak?
Let's look at the first feat you listed.
315 lbs is a very respectable number but far from record breaking. Arthur Saxon lived at the turn of the 20th century. He lifted 370 lbs over his head with one hand, and there are reports of him doing even more. The lift is called bent press. Eugen Sandow is a contemporary of his who also did the lift but couldn't reach the Greek's numbers. Eugen managed around 275 lbs.
Eugen unlike Arthur was always weight conscious and had a very lean physique. As you know, strength in strongman lifts is correlated with height and weight. The Greek might have had better conditions to start with.
The two strongman I mentioned lived when there weren't even bench presses yet. They certainly didn't benefit from today's advances.
The other feat is too ambiguous to compare. It would already be a feat to simply budge the stone. At no time would the stone be lifted off the ground then. And even if the stone were elevated, it's not comparable to a deadlift. Deadlift records only get recorded for successful lifts that reach full extension. Take a look at failed deadlift attempts. They accomplish the lift off from the ground but fail because no full extension is achieved. If there were competitions in which a weight only needed to be lifted for an inch, you'd see much more impressive lifts.
That story about Milo and the Cow is a great myth. Long story short, elite powerlifters need to constantly cycle back their training with a deloading week in order to not burn themselves out.
edit: it's quite a big topic. Here's one source: http://www.ncbi.nlm.nih.gov/pubmed/3683452