As someone who works in Flatlands and lives near Kensington, I commend you on your fine topic. Given that it is pretty broad for a virtual reference query, I'm going to point you in some directions, and hopefully you'll have time to explore and do some research and reading to hone your timelines.
Perhaps your first visit could be to Brooklyn Public Library's Brooklyn Collection, which is the local history department. The branches in your target neighborhoods may also have some archival materials you could look through (for example, at the Flatlands branch we have a drawer full of clippings and documents that may or may not cover the types of events you're interested in). And of course you should visit the Brooklyn Historical Society.
Read blogs about Brooklyn neighborhoods and history to pick out details of local social movements and also to find evidence of community groups that may still be active and have memories (either institutional or physical, in the form of people who were around back in the day) of events relevant to you. Try the blogrolls of Brooklynology and the Brooklyn Historical Society Blog as starting points. Neighborhood cultural spaces could also be helpful -- for example, Bed-Stuy's Restoration Plaza recently hosted an exhibit of photos of neighborhood protests and other community events from the 1960s through '80s (link to a New York Amsterdam News article here).
As for the particular events you mentioned, there are several books that cover the Ocean Hill-Brownsville teacher strike. A quick search of WorldCat finds many titles that will be available in the NYC public library systems or via interlibrary loan. There's less documentation of the Beth-El Hospital strike (you were right about the year, by the way), but there is some (ignore the record for Pediatric Acupuncture, which clearly has the wrong contents note).
The following books may focus too much on pre-1960s pictorial histories, but you could also try books by local historian Brian Merlis and the "Images of America" series.
The NYC CityMap can be a good beginning source of information about individual lots, vacant or otherwise. A specialized source that you may already be aware of is Picture the Homeless's Vacant NYC map. A PTH staffer explained that most of the data on vacant lots has come from Freedom of Information Law (FOIL) requests to the division of real estate services and from the Mayor's Office of Environmental Remediation's Searchable Property Environmental E-Database (SPEED) Portal.
On a more general note about the relationship between municipal operations and usable data, PTH's Homeless People Count report says: "While many city agencies keep track of information on buildings, we received no response when both Picture the Homeless and the Manhattan Borough President's Office attempted through numerous channels to obtain property information from such public entities as HPD, DOB, Con Ed (which should keep track of all buildings to which power had been turned off entirely, and for how long), the Department of Sanitation (for records of residential units to which water had been turned off), and even the Fire Department. As a result, we were obliged to undergo a painstaking research process that involved looking up every building in a series of city databases." That database research is, of course, in addition to the hitting-the-streets methodology that made up the bulk of the process (a PTH staffer described the vacant lot count as "just people canvassing with notepads").
Well, as I said, this answer is meant to provide a number of starting points, but please follow up if you hit snags with more specific questions -- or if you just want to let us know what you uncovered!