ZBW Air Traffic Controller reported situation of weather; volume and another facility not taking hand-offs without prior coordination resulted in the controllers scrambling to keep aircraft in their airspace and to find a route for the aircraft to be assigned.

Narrative

I was instructed to sit at RA10 as the upcoming numbers suggested sector 10 was going to be over saturated with traffic. Immediately I could not get a proper briefing done due to having to coordinate for the R side for many things throughout the sector so they were able to stay on frequency. The minute things went south fast was ZOB reached out and said ZNY was no longer taking IAD at any route; while we have 2 flashing at them within two minutes of their boundary. Not only did this leave us scrambling to start vectoring and coordinating for the now 3 aircraft going to IAD and having to get them new routes. Due to weather and volume only one route along the coast was open. We uploaded the route to the three aircraft and all three complained of fuel concerns due to being international flights. All while this was going on the sector started to become saturated with traffic from all directions. Planes stepping on top of each made things impossible and frustrating. Within not even five minutes of the new route uploaded we were then told the only route out was closed. We then frantically had to divert two planes to their alternative airports due to fuel concern. At this point some of the planes had well been inside of Sector 38s airspace all with coordination but it was a mess. Not even later than 9 minutes of all this going on ZNY opens routes to IAD via PSB 30 miles in trail. Which is complete and utter sloppy work. What in the 9 minutes that changed allowed them to now take the current traffic load. No facility should have the availability to shut routes on and off without any sort of plan. Not only is it unsafe but completely selfish when it comes to working as a team. This sort of things happens OFTEN with ZNY and deserves to be looked into with a full investigation. Lives at stake with our job and it seems like this was a failure of the NAS as a whole. From TMU (Traffic Management Unit) to the supervisors; to the controllers who think they can handle a heavy workload so breaks can keep on flowingRecommendation: COMMUNICATION FROM TOP TO BOTTOM. The NAS is slowly starting to crack with the amount of planes and low staffing at all these facilities. There's too much traffic in the sky to continue pushing these planes in the sky. I'm just a trainee and so I don't have much experience to provide guidance. But the one thing I do see is the system is outdated; old; and unreliable. New ways of communicating needs to be done.