If Sludge Strider and another artifact enter the battlefield 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 the battlefield under your control, Sludge Strider's ability will trigger a total of twice: Once when that creature enters the battlefield, 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.