If Sludge Strider and another artifact enter under your control at the same time, Sludge Strider's triggered ability will trigger. Similarly, if Sludge Strider and another artifact you control leave the battlefield at the same time, Sludge Strider's triggered ability will trigger.

If an artifact creature with 0 toughness enters under your control, Sludge Strider's ability will trigger a total of twice: Once when that creature enters, and once when it's put into a graveyard. Both abilities will be put on the stack after the state-based action check that puts the 0-toughness creature into the graveyard is finished.