What are the figures of speech used in each line of Jaques' "seven stages" speech in As You Like It?

Jacques' speech in II.vii of "As You Like It" is rife with literary devices. Before jumping into a line by line analysis, it is important to note some figures of speech that span the entirety of the speech. These are personification and irony. Personification is the assigning of human qualities or actions to non-human things. In this case, time is being given human characteristics - the infant, the schoolboy, etc. The speech is ironic due to its self referential nature - the character of Jacques is referring to the world as a stage while the actor playing Jacques is speaking these words on an actual stage. There is a meta-theatricality to this that we find often in Shakespeare (Hamlet's instruction of the players, Fabian's proclamation: "If this were played upon a stage now, I could condemn it as an improbable fiction," to name a few). 

The speech is also full of imagery. You can easily pick out the images created by Jacques' detailed description of each age.

As for a line-by-line dissection of the rhetoric:

All the world's a stage,
And all the men and women merely players;
They have their exits and their entrances,
And one man in his time plays many parts,
His acts being seven ages.

                               At first the infant,
Mewling and puking in the nurse's arms.
Then, the whining school-boy with his satchel
And shining morning face, creeping like snail
Unwillingly to school.

Alright. Metaphor is still working here. We also have a simile pop in with "creeping like a snail" - a comparison between the school boy and a snail intended to illustrate the boy's pace. There is some alliteration working here as well (the repetition of consonant sounds at the beginning of words) - school-boy, satchel, snail, school.

                             And then the lover,
Sighing like furnace, with a woeful ballad
Made to his mistress' eyebrow. Then, a soldier,
Full of strange oaths, and bearded like the pard,
Jealous in honour, sudden, and quick in quarrel,
Seeking the bubble reputation
Even in the cannon's mouth.

We have another simile here with "sighing like a furnace" - comparing the sighs of a lover to the sounds made by a furnace. We also have some more alliteration with "quick in quarrel." There is another metaphor layered under the extended metaphor that is the entire speech in the line "seeking the bubble reputation." Here, reputation is compared to a bubble, something that rises quickly, and pops abruptly with the slightest pressure.

Cannon's mouth is an instance of metonymy - a figure of speech in which a word is replaced by a thing that is closely associated with it (think, "the pen is mightier than the sword" - "pen" and "sword" replace "words" and "violence," the pen and the sword being the tools of the words they are replacing). Cannon's mouth here is being used in place of battlefield or war or conflict.

And then, the justice,
In fair round belly, with a good capon lined,
With eyes severe, and beard of formal cut,
Full of wise saws, and modern instances,
And so he plays his part.

In these lines, we have some hyperbaton - the inversion of normal word order. "In fair round belly, with a good capon lined, with eyes severe, and beard of formal cut" - these phrases are sort of jumbled around, possibly to mimic the way a justice might speak. 

                          The sixth age shifts
Into the lean and slippered pantaloon,
With spectacles on nose and pouch on side,
His youthful hose, well saved, a world too wide
For his shrunk shank, and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound.

We have an example of ellipses in this section in the line "with spectacles on nose and pouch on side" - an ellipsis is an omission of words. We are missing the word "his" twice in this line (with spectacles on his nose and pouch on his side). We have another instance of alliteration with "shrunk shank."

Last scene of all,
That ends this strange eventful history,
Is second childishness and mere oblivion,
Sans teeth, sans eyes, sans taste, sans everything.

This final section has some sophisticated rhetoric. We have parenthesis with the line "That ends this strange eventful history." A parenthesis is a self-interruption within normal word flow. This particular parenthetical moment is an example of appositio, or an insertion of an explanation or description.

In the final line, we have an example of a diacope with the repetition of the word "sans" - diacope is generally used to convey big feelings and specifically refers to the repetition of a word or phrase with one or more words in between.