Why is Sheshnag considered more powerful than Arjuna in Hindu mythology, and what are some examples of his strength?

 Both Sheshnag and Arjun were invincible who stood against their own relations to establish Dharma ( righteousness) on Earth.

Sheshanag was Kadru’s son who had enslaved her sister Vinata with deceit. Majority of his brothers helped their mother in conniving. Like the Kauravs they too were innumerable. Vinata’s only living son Garuda freed his mother from captivity. Sheshanag left his brothers and undertook hazardous expedition to mount Gandhamadana to atone for the sins his mother had committed and he was unwittingly part of it.

“And Sesha replied, 'My uterine brothers are all of wicked hearts. I do not desire to live amongst them. Let this be sanctioned by thee. Like enemies they are always jealous of one another. I am, therefore, engaged in ascetic devotions. I will not see them even. They never show any kindness for Vinata and her son. Indeed, Vinata's son capable of ranging through the skies, is another brother of ours. They always envy him. And he, too, is much stronger owing to the bestowal of that boon by our father, the high-souled Kasyapa. For these, I engaged in ascetic penances, and I will cast off this body of mine, so that I may avoid companionship with them, even in another state of life.”

SECTION XXXVI Astika Parva K M Ganguli’s Mahabharat

Brahma entrusted Shesha with the task of keeping the Earth stable, something far beyond any mortal’s ability.

"Brahman said, 'O Sesha, I am exceedingly gratified with this thy self-denial and love of peace. But, at my command, let this act be done by thee for the good of my creatures. Bear thou, O Sesha, properly and well this Earth so unsteady with her mountains and forests, her seas and towns and retreats, so that she may be steady.'

SECTION XXXVI Astika Parva K M Ganguli’s Mahabharat

He is an eternal being hence called Ananta Shesha, while Arjuna is unparalleled among humans.

"Sauti continued, 'The snake, Sesha, the lord Ananta, of great prowess, lives underneath the Earth, alone supporting the world at the command of Brahman. And the illustrious Grandsire, the best of the immortals, then gave unto Ananta the bird of fair feathers, viz., the son of Vinata, for Ananta's help”.

SECTION XXXVI Astika Parva K M Ganguli’s Mahabharat

Sheshnag is divine and immortal. He supports the Earth and displays strength far exceeding Arjuna’s.

picture from online source