According to Classical Theravada (that is, the Pali Canon as interpreted by the Commentaries and the Visuddhimagga) the three deliverance just refer to which of the three characteristics is the most prominently contemplated the mind to attain enlightenment, and there isn't much of a practical difference.
The eight liberation are mostly an alternate way of describing the progression of samadhi. You can describe it in a lot of different ways, the Jhanas are just one way of talking about it.
You also ask how to switch to the contemplation of the five aggregates after attaining concentration, especially using anapanasati. The most general description of this is given in the Visuddhimagga:
One who wants to accomplish [insight], if, firstly, his vehicle is
serenity, should emerge from any fine-material or immaterial jhána,
except the base consisting of neither perception nor
non-perception, 3 and he should discern, according
tocharacteristic, function, etc., the jhána factors consisting
of applied thought, etc., and the states associated with them, [that
is, feeling, perception, and so on]. When he has done so, all that
should be defined as “mentality” (náma) in the sense of bending
(namana) 4 because of its bending on to the object.
Then, just as a man, by following a snake that he has seen in his
house, finds its abode, so too this meditator scrutinizes that
mentality, he seeks to find out what its occurrence is supported by
and he sees that it is supported  by the matter of the heart.
After that, he discerns as materiality the primary elements, which are
the heart’s support, and the remaining, derived kinds of materiality
that have the elements as their support. He defines all that as
“materiality” (rúpa) because it is “molested” (ruppana) [by cold,
etc.]. After that he defines in brief as “mentality-materiality”
(náma-rúpa) the mentality that has the characteristic of “bending” and
the materiality that has the characteristic of “being molested.”
In other words, after attaining concentration, your switch your object of meditation to the mental qualities in the mind caused by such concentration. You put your attention on and observe the qualities of peace, clarity, joy, etc... and see them very clearly. After that, you turn to the body, watching and observing the physical sensations of the body such as hardness, cohesion, movement, heat, etc...
If you want detailed instructions on how to do this especially for Anapanasati, this section of Ajahn Buddhadasa's book on Anapanasati is one of the best in my opinion: http://www.dhammatalks.net/Books3/Buddhadasa_Bhikkhu-Anapanasati-Fourth_Tetra.pdf