Borderlands – What do I do with Eridium after maxing out the SDUs

According to the Borderlands 2 Wikia page related to Eridium:

So far it is unknown if there is a sure-fire way to obtain Eridium, but it is an uncommon-rare drop by certain enemies and rarely found in containers like lockers and washing machines. You can also obtain it by playing the slot machines at Moxxxi's place in Sanctuary.

Moxxxi's slot machines

According to this article the following is a list of potential payouts from playing the slot machines - in addition to randomly generated weapons and items of course;

• x3 Bandits: Live grenade (Run!)
• x3 7s: Customization skin
• x3 Cherries: Green item
• x3 Legs: Blue item
• x3 Marcus: Purple item
• x3 Borderlands logo: Orange item
• x3 Eridium Bar (1): 4 Eridium
• x3 Eridium Bars (2): 8 Eridium
• x3 Eridium Stack (3): 16 Eridium (!!!!)
• Any two with non-bell: White weapon
• Any two with bell at end: Cash

It is worth noting that playing the slot machines at Moxxxi's place will get more expensive as you progress through the game, yet some of the items you can win by playing the slots scale with your character - this means that playing the slots at a lower level will cost less while still potentially providing benefit to you at the later levels.

You can spend Eridium once you get to Sanctuary. Crazy Earl runs the black market. It's not hidden or anything: it's just one of the stores available in town.

Once you've bought everything from Crazy Earl; there is a boss monster, Terramorphous, that will cost 4 Eridium to fight again. (source)