If you decide your algae is living on your orcs, you are defining a commensalism, not a symbiotic relationship.
As a human, algae, specifically blue green is toxic to humans. So if this is the algae you are using, your orcs will need a tolerance to the toxins emitted by the algae.
Algae also comes in forms like kelp which can grow to hundreds of feet in length.
Sticking with a symbiotic relationship, your orcs could provide expanded environments for their algae farming enterprises. Having caretakers, the algae could have a variety of forms it takes when grown in particular conditions that produce foods and medicines for your orcs. Consumption or using these as ointments etc, would contribute to the "green" of your orcs.
Maybe one version of algae is brewed into a popular alcoholic drink. Consuming it could cause bioluminescence or phosphorescence. Maybe your orc Mardi gras is a "glowing" spectacle.
Kelp could be a form of clothing or armor that "grows" giving the orcs a special kind of protection and does something in combat that is advantageous to make and wear algae armor.
The more "uses" your orc society makes of the algae grown, harvested, processed into products, the greener they become, the more dependent on the algae activities they would be.
Your orc shaman might smoke certain algae that gives them "visions", or special insights. Dune harvested spice to warp space time. Maybe not quite that level, but it could be useful in your storyline.
Final note: Orcs from Tolkein and other references aren't actually green, they are more grey.