How do the Titans of Greek mythology relate to the Odyssey?I'm interested in specific examples and explanations.

Look no further than Book I:

Tell me, O muse, of that ingenious hero who travelled far and wide
after he had sacked the famous town of Troy. Many cities did he visit,
and many were the nations with whose manners and customs he was acquainted;
moreover he suffered much by sea while trying to save his own life
and bring his men safely home; but do what he might he could not save
his men, for they perished through their own sheer folly in eating
the cattle of the Sun-god Hyperion; so the god prevented them from
ever reaching home. Tell me, too, about all these things, O daughter
of Jove, from whatsoever source you may know them.

Hyperion is mentioned 4 times, namely when Odysseus' men eat his cattle.  In Book XII:

'You will now come to the Thrinacian island, and here you will see
many herds of cattle and flocks of sheep belonging to the sun-god-
seven herds of cattle and seven flocks of sheep, with fifty head in
each flock. They do not breed, nor do they become fewer in number,
and they are tended by the goddesses Phaethusa and Lampetie, who are
children of the sun-god Hyperion by Neaera. Their mother when she
had borne them and had done suckling them sent them to the Thrinacian
island, which was a long way off, to live there and look after their
father's flocks and herds. If you leave these flocks unharmed, and
think of nothing but getting home, you may yet after much hardship
reach Ithaca; but if you harm them, then I forewarn you of the destruction
both of your ship and of your comrades; and even though you may yourself
escape, you will return late, in bad plight, after losing all your
men.'

Atlas is also mentioned in Book I:

It is an island covered with forest, in the very middle of the sea, and a goddess
lives there, daughter of the magician Atlas, who looks after the bottom
of the ocean, and carries the great columns that keep heaven and earth
asunder. This daughter of Atlas has got hold of poor unhappy Ulysses,
and keeps trying by every kind of blandishment to make him forget
his home,

The Titan Oceanus is mentioned in Book IV:

"'The third man,' he answered, 'is Ulysses who dwells in Ithaca. I
can see him in an island sorrowing bitterly in the house of the nymph
Calypso, who is keeping him prisoner, and he cannot reach his home
for he has no ships nor sailors to take him over the sea. As for your
own end, Menelaus, you shall not die in Argos, but the gods will take
you to the Elysian plain, which is at the ends of the world. There
fair-haired Rhadamanthus reigns, and men lead an easier life than
any where else in the world, for in Elysium there falls not rain,
nor hail, nor snow, but Oceanus breathes ever with a West wind that
sings softly from the sea, and gives fresh life to all men. This will
happen to you because you have married Helen, and are Jove's son-in-law.'