This is a good question. First, if you've ever used a kerosene or oil lantern or lamp, you'll have noticed that the wick needs to be set high enough to provide decent flame for light, but if set too high it makes soot. Any lamp needs to be tinkered with, to make it burn clean ( and yes, if you try making a torch, of the peasants-in-revolt kind, you'll find they make soot very, very well). Second, there are lots of fats that will burn in a lamp, but some- like beef tallow- are solid at slightly-low temperatures, which makes them hard to use, and some vegetable oils are acidic enough to oxidize and turn into varnish, like linseed oil. Wax candles are good, but you can't make a big flame with a candle, you have to simply multiply candles, which can be awkward if you don't have space for a chandelier. So, it was not without reason that people wandered the ocean in sailing ships for five years at a stretch, looking for whales. It was better than most everything else.

There was actually a good bit of processing of whale oils. The blubber would have to be boiled in trypots, to get the oil out, then the barrels of oil would be left outside in the winter until they congealed, and the congealed mass pressed to extract the liquid, which would be Number 1 Whale Oil . This would have a slightly fishy smell, be used in lamps. If it was a sperm whale, the head or "case" would supply a much lighter oil, called Sperm Oil. This was very fine, and for the 18th and early 19th centuries the best oil for lubricating watches and other fine machinery. The oil that did not make the grade of Number 1 would be mostly used for soap making, having too much fatty acid to be stable without spoiling. If somebody tried to use it in a lamp, it would likely smell very strongly of fish, tend to solidify in the cold.

Note that seals were also hunted and turned into oil: this was often mixed with whale oil and burned in lamps, and it was impossible to tell if this had been added.

Lekowitsch:Chemical Technology of Oils, Fats and Waxes, 1904