Halak stopped 24 of 27 shots in Sunday's loss to the Kings.
Nelson had the game-winning goal Saturday against the Sharks.
Halak will defend the cage for Sunday's clash with the Kings in Los Angeles.
Pulock has yet to play for the Islanders this season.
Greiss set aside 40 of 41 shots in Saturday's 3-1 road win over the Sharks.
Beauvillier wasn't included in the lineup for Saturday's matchup in San Jose, Arthur Staple of Newsday reports.
Clutterbuck (hip) is in the lineup to take on the Sharks on Saturday, Arthur Staple of Newsday reports.
Beauvillier has only one a single goal and no assists in four games to start the season.
Clutterbuck (hip) will be a game time decision Saturday versus the Sharks, Arthur Staple of Newsday reports.
Eberle (undisclosed) declared himself ready to play in Saturday's road game against the Sharks. "It felt good during morning skate," he said. "I'm ready to go and excited to get back."
Mayfield has an assist, six penalty minutes, three shots on goal and is a plus two in three games so far this season for the Islanders.
According to coach Doug Weight, Clutterbuck (lower body) is expected to return to the lineup for Saturday's game against San Jose.
Greiss will get the starting nod for Saturday's tilt versus San Jose.
Eberle's status is uncertain for Saturday night's contest after taking a hard hit in Thursday's practice.
Clutterbuck (lower body) has been ruled out for Wednesday's clash with Anaheim, Arthur Staple of Newsday reports.
Greiss stopped 33 of 35 St. Louis shots on Monday in a 3-2 shootout loss.
Ladd's goal in the third helped his team earn a point in a 3-2 shootout loss to St. Louis on Monday
Halak will start Monday's tilt against St. Louis, Brian Compton of NHL.com reports.
Clutterbuck (lower body) will travel with the team on its three-game West Coast trip, but won't be available Monday against St. Louis, Brian Compton of NHL.com reports.
Greiss will defend the cage for Monday's clash versus St. Louis.
Clutterbuck (lower body) has been ruled out for Saturday's home tilt against the Sabres, Arthur Staple of Newsday reports.
Ho-Sang will make his season debut Saturday versus the visiting Sabres, Arthur Staple of Newsday reports.
Bailey (personal) is projected to play Friday night against the host Blue Jackets, NHL.com reports.
Halak will be the starter for Saturday's home game against the Sabres.
Greiss will guard the cage Thursday night against host Columbus.