The origin of these words is Latin for east and is still used in Romance languages to indicate a compass direction.
In English:
.
"Oriental" is a less-used (and considered offensive by some) word describing a person or object with origins in the Asian continent. The more respectful term these days is "Asian".
"Orient", when used as a verb, means to identify one's location in relation to other features. Example:
"I stepped out of the building's entrance and took a moment to orient myself before heading in the direction of the plaza."