Universal Quests are not restricted to one race. If you can reach the Quest NPC you can receive the quest, and if you can stay alive in the area to do whatever the quest requires, you can complete it regardless of your race. Quests from Elim and Shugo that do not require actions which you cannot perform are all Universal.
A very few of the quests listed on this page simply have two versions, one for each race, with the same name. A New Skill is an example. You cannot do both.