If a unit cannot move like by Vex's ability, can it be moved by a spell or ability?

No.

If a unit is restricted from moving by an effect such as Vex, Apathetic's ability, it cannot be moved by any means, including spells or abilities.

According to the RiftJudge FAQ (id 10516) regarding Vex, Apathetic:

• The movement restriction imposed by Vex is "absolute for that turn."
• It does not distinguish between a Standard Move and a move caused by a card effect (like Ride the Wind).

While move effects from spells or abilities normally bypass restrictions that apply to Standard Moves (such as Ganking or the requirement to exhaust), they cannot override an explicit, absolute restriction placed on a unit by an ability like Vex's.