It's hard to say WRT your examples; while the trireme only had one man to an oar, there's still a lot of debate how larger Hellenistic era warships were organized and rowed, so it's hard to give a definitive answer, and the Vikings are outside my area of interest. I do know about 16th century war galleys, though, so hopefully shit should still be interesting. In short, it wasn't as much strength as skill that determined your position on the rowing bench.

During the 16th century, there were two main systems for rowing warships. In the beginning, all of them were rowed alla sensile, with each rower pulling his own oar. The typical galley had 24 banks of oars on each side, and three rowers to a bank, for a total of 144 oarsmen. This system made for light, agile ships; they were able to dash in quickly under oars for boarding actions and shore raids, and could cruise through the Mediterranean on long distance voyages of piracy and extortion, resupplying themselves on plunder along the way. However, it had its limitations. Making larger ships, able to carry greater weight of artillery and deck fighters, was difficult when each oarsmen needed the space to work his own oar; the further in the ship you get, the less efficient the stroke, and with relatively small individual oars, this means a lot of energy is wasted. Moreover, with each man in charge of pulling his own oar, you needed 144 people who could keep time with the rest of the crew, or else waste their energy rowing out of time. When warfare was relatively small scale and manpower thus relatively plentiful, this was less of an issue.

However, from the beginning of the 16th century, the previously compartmentalized naval wars of the Mediterranean -Spain's wars with North African corsairs, Genoa's rivalry with Venice, the Knights of Rhodes' raids on Ottoman shipping- found themselves increasingly subsumed into a grand imperial rivalry between the Ottomans in the east and the Habsburgs in the west. These Renaissance superpowers consolidated their control domestically, crushing internal resistance and building bureaucracies to marshal ever greater resources, and thus extended their reach abroad. The African corsairs became auxiliaries of the Ottoman sultan, while Genoa and the Knights of Rhodes found themselves drawn into Habsburg Spain's orbit. Venice spent much of the century attempting to stay aloof, but was drawn into the fray several times. This process reached the point that it has been estimated between 70% and 90% of all warships afloat in the Mediterranean were concentrated at a single point on a single day for the apocalyptic battle at Lepanto.

In this new strategic environment, skilled manpower became a precious commodity. We're no longer talking about a dozen galleys sent out to take slaves and hostages from coastal villages, but fleets of hundreds of ships sent against major strategic objectives. When Charles V made the Mediterranean a key battleground in his imperial rivalry with the Ottomans, he descended on Tunis with 74 galleys (requiring more than 10,000 oarsmen) and hundreds of sailing ships; the Ottoman fleet at the Battle of Preveza three years later was more than 120 ships (17,000+ rowers). At Lepanto, they brought perhaps 40,000 rowers in a fleet of more than 200 full sized galleys; they were butchered almost to a man in the ensuing battle, but three years later the Ottomans sailed an even larger fleet of 300 ships 1500 miles from Constantinople to Tunis, capturing the Spanish fortress there in a dazzling strategic coup, the last of its kind.

The naval powers of the era relied on recruiting people already skilled in their occupations; by and large, they did not train men to be sailors in the sense of instructing them in unfamiliar skills. Even though the role of rowers was not quite as complex as that of skilled sailors, the number of free men available to risk their lives in fetid galleys was finite, and could not support warfare on this scale for long.

As the scale of warfare was increasing, so to did the price of waging war. Fueled by the great influx of precious metals from the new world, prices through the century skyrocketed. The most important expense for galley captains was the ship's biscuit; the price of this commodity quadrupled over the course of the century. Every effort had to be strained to reduce costs.

These two trends drove most naval powers in the 16th century to adopt the scaloccio arrangement for their oarsmen. Here, each oar was pulled by several rowers at once. This had some notable effects. To finally address the core of your question, it allowed the limited free manpower of fleets could be stretched further with this system, as with a team of oarsmen, only the leader needed to keep pace with the rest of the complement, providing the aim and impulse to the oar, while several slaves or convicts simply put their backs into it. As the further from the outriggers you get in the ship, the longer the sweep of the oar gets, the leader of each bank of rowers needed to not just pull his oar, but get off his bench and step forward to keep his hands on it, returning to the seated position during the stroke.

With free manpower requirements limited, the rising expenses of fleets could be mitigated by finding cheaper unskilled manpower; slaves, debtors, and convicts are not prime sailors, but they have strong enough backs, and are significantly cheaper than hiring free men. While galley wars remained astronomically expensive by the standards of the day, they remained were still possible to fund; attempting to stick to manning them with free oarsmen would have significantly inhibited warfare.

As the number of free, skilled oarsmen needed was now limited to the number of benches rather than oarsmen as such, galleys could be made much larger than ever before while still retaining dash speed for combat. Whereas the earlier vessels had kept to three men to a bench, the new scaloccio system allowed more than six to work a single oar. Larger ships carried more marines and more firepower. Complements of oarsmen grew from 144 to more than 200 by 1571; at Lepanto, the Spanish flagship Real had more than 400 oarsmen and as many marines, and the Ottoman Sultana matched it almost exactly.

With higher freeboards, more marines, and better artillery, a Spanish galley of 1571 was a vastly more powerful machine than it's 1535 counterpart. However, this was not achieved without cost. All these improvements were made possible by an increased crew of oarsmen. These men had to be fed and watered, and the space they take up on the ship is space that can't be used to store provisions. While individual galleys could resupply themselves on plunder, this was impracticable for the large fleets needed for important strategic undertakings; their radius of action became increasingly limited by how much food they could store for their bloated crews. As the tactical power of the galley increased, its strategic usefulness declined, until it was a glorified harbor and coastal defense craft.