Is orbital celulitis contagious?

No. Cellulitis by itself is an infection/inflammation of the soft tissue under the skin. It is usually contained and not contagious. If it turns into an abscess with drainage, that fluid could transmit infection by direct contact. Regardless, try not to touch any areas of infection with bare hands and adopt an aggressive hand washing routine to prevent spread of bacteria/viruses.
No. Periorbital cellulitis is bacterial infection of the tissues surrounding the orbit and can be medical emergency because of possible extension into the orbit or intra cranially via the optic nerve. But not contagious.