Here is a tweet from NASA flight director Royce Renfrew's personal twitter account. I believe at least some of the Hurricane Harvey OPS team is on-site at Johnson Space Center but the work might be distributed. What kind of tasks and challenges does the Hurricane Harvey OPS team have? What's been going on there during the hurricane and its aftermath?
The 'Hurricane Harvey ops team' is a subset of the flight operations team. They've kept working in the Mission Control Center while all other personnel has been sent home.
Challenge: being cooped up in the office for several days with a hurricane going on outside, possible utility interruptions due to storm damage.
Despite the crisis unfolding flooding outside, ISS flight directors and more than 100 other “essential” personnel have ridden out the storm inside JSC’s iconic Mission Control Center to maintain watch over the ISS.
Another flight director described the scene as surreal, with off-duty teams sleeping in a backup flight control room. Pictures showed cots lined up in front of a Flight Dynamics Officer’s console.
Thanks in part to the team’s sacrifice, Harvey has caused no disruption to space station operations.
There's a backup flight control center:
In one precautionary measure, downlinks of science research video has been rerouted to NASA’s Marshall Space Flight Center in Huntsville, Alabama, which can serve as a backup Mission Control Center in an emergency.
(this was part of my initial answer, leaving it here because it's interesting)
For hurricanes etc., NASA assigns a rideout team to various locations. The rideout team watches the site for damage, tries to mitigate it and decides when it's safe for other personnel to enter the base.
Members of a 139-member “rideout” team will be stationed at various facilities across the space center to monitor critical systems “and report any significant events” to emergency operations personnel in the Complex 39 Launch Control Center where space shuttle launchings were once managed.
“After the hurricane has passed, and winds have dropped below 50 knots, areas around KSC will be assessed and the damage assessment and recovery team will report for duty,” Diller said.