What effect does the rhyme scheme AAAA(1st stanza), AABB(2nd stanza), and AABBB(3rd stanza) have on the poem "The Mask of Anarchy" by Percy Bysshe Shelley in terms of tone and how the reader perceives the writing?

Rhyme schemes like AAAA and AABB are rather simple rhyme schemes. The scheme AABB is a particularly common one, sometimes seen in nursery rhymes or children's poems, even. Because of its simplicity, the AABB set-up can read as somewhat "sing-songy," and can lend an air of innocence to a poem. In this sense, the use of AABB in Percy Shelley's Mask of Anarchy is rather ironic since the subject matter of the poem is anything but innocent. Let's look for example at stanzas 2 and 3, which are both in AABB rhyme scheme:

2I met Murder on the way--He had a mask like Castlereagh--Very smooth he looked, yet grim;Seven blood-hounds followed him:
3All were fat; and well they mightBe in admirable plight, For one by one, and two by two,He tossed them human hearts to chew

The meter is not quite as predictable or simplistic as we sometimes see in nursery rhymes or children's poems; however, we see a basic, straightforward AABB rhyme scheme: way and Castlereagh in lines 5 and 6, grim and him in lines 7 and 8, and so forth. The content of these lines, though, is not innocent or simplistic. The speaker meets "Murder" personified, accompanied by "Seven blood-hounds." This is clearly an ominous image, which is then continued in stanza 3 when "He tossed them human hearts to chew." Early in the poem, despite the simple rhymes, Shelley creates a frightening and foreboding mood. Most of the poem continues in this four-line, AABB structure and rhyme.
The AAAA rhyme in stanza 1 is a bit different, since there is the same end rhyme for each line. Shelley writes,

As I lay asleep in ItalyThere came a voice from over the Sea,And with great power it forth led meTo walk in the visions of Poesy.

The AAAA scheme can sound monotonous since it relies on only one sound. Here, though, the stanza serves as a short prelude to the story that the poet is about to tell. The transition into a different rhyme scheme in stanza 2, then, is appropriate, as it marks a shift into the narrative proper.
In stanza 4, the poet writes 5 lines in a different scheme of ABBCC (just based on this stanza, not considering previous rhymes). It's odd, as well, because the first line of the stanza actually goes along with the previous stanza and rhymes with lines 11 and 12 (two, chew, and drew):

Which from his wide cloak he drew.Next came Fraud, and he had on,Like Eldon, an ermined gown;His big tears, for he wept well,Turned to mill-stones as they fell.

It is unclear why Shelley would put this line, which belongs in rhyme and theme to the previous stanza in stanza 4. Perhaps it is to serve as a more seamless link into the next personified character, Fraud. Then, the rhyme changes with the new character. There are other instances of five-stanza sections in the poem, but they are not used as often as the four-line AABB scheme.
Generally speaking, Mask of Anarchy is a rather dark poem detailing the frightening arrival of Anarchy and his supporting cast (including Murder and Fraud, among others). As such, the simple, sometimes song-like rhyme contrasts with the more mature and foreboding imagery.