The sages (as the series calls them) are based off the Shichi Fukujin (the Seven Gods of Luck and Fortune).

In this particular game they are hidden in 5 spots throughout the game.

Stage 1: shoot a particular frog a number of times Stage 2: defeat the bomb-hurling kappa on the raft Stage 3: tail whip a specific gravestone (see Akisto's run to know which one) Stage 4: shoot a particular vulture a number of times Stage 5: shoot a particular fireplace

Which one you get depends on what frame you hit "start" during the cutscene before the levels themselves. This is very important to learning the game as a speedrun as bombs have the capability to destroy most boss fights making them essential for a getting an optimal time and only 3 out of 7 of them drop a bomb.

Ebisu:

The God of fishing, shipping and commerce will give you an upgrade to either one of your spreader or fire weapon as well as some health. Sadly, not very useful drops for the speedrun (upgrading/renewing your level 3 weapon aside).

Daikokuten:

The God of wealth and prosperity. Same drops as Ebisu so the same sentiment applies here.

Bishamonten:

The God of warriors. Same drops as Ebisu and Daikokuten so the same sentiment applies here.

Fukurokuju:

The God of wealth, happiness and longevity. Same drops as Ebisu, Daikokuten and Bisamonten so the same sentiment applies here.

Jurojin:

Unlike the first 4 sages mentioned above, Jurojin (the God of wisdom) drops health, a bomb and a magical shield. Bombs are integral to the speedrun but the health and the shield are nice to add to that as well.

Hotei:

The God of happiness and abundance offers the same drops as Jurojin so this is another sage you want in a speedrun.

Benzaiten:

The Goddess of arts and knowledge and unquestionably the most important of all 7 sages in the speedrun. On top of the usual health drop, she drops a bomb and the unique mad dog. The mad dog grants you complete invincibility for a short period of time and destroy anything that stands in your way.

The mad dog can get you killed in stage 2 so getting her in that level is not the best situation but in stage 5 she is vital (moreso than Hotei and Jurojin) as doing the last stretch of stage 5 fast while avoiding death is very hard without mad dog since the magical sheild offers no protection to the spike balls in that particular level.