There are only three Emergency Units running now E-1 is at Woodward Ave with Engine 5, E-2 is at Howard Ave with Engine 11 and Truck 2, and E-3 was activated at Ellsworth with Engine 9. Both Squad 1 and Squad 2 are now disbanded, they merged into Rescue 1, Emergency 3 and also the SOC. Squad 1 was running with the new Rescue 1 for a short time I guess before the full transition to the present operations from what I was told. As for Emergency 4, it would be nice to see it reactivated as they can justify the additional medic unit. However I don't know if they have the personnel to staff it.
Back when there were 4 Emergency Units, 3 of them were BLS E-1, E-2 & E-4 (C-MED 1-Alpha- 1, 2 & 4) and E-3 (5-Alpha-3) was ALS only. You were close with the assignments, I don't member exactly which unit was at which station, but they were located at Headquarters (Grand Ave), Ellsworth Ave, Whitney Ave and Howard Avenue. I was working at C-MED New Haven when Emergency 1, 2 & 4 were deactivated and E-3 was moved to Grand Avenue, and eventually re-designated Emergency 1. This is when NHFD began transitioning the Engine Co.'s to respond as the BLS first responders. While all 4 emergency units were active, the Engines would not respond to EMS calls out side of their district, with some exceptions (and problems). When NHFD realized the need for two medic units, they moved Emergency 1 over to Woodward Avenue and re-organized Emergency 2 out of Howard Avenue, this happened around 2002 roughly.
Also at this time is when they organized Squad 1 and Squad 2. Engine 8, originally the Pierce / Ford pumper running with the old International Tactical Unit 1 when needed, was outfitted with the original Pierce rescue pumper since they were the city-wide extrication unit (Truck 2 also has tools on it for I-95). When Squad 1 was organized, Engine 8 reverted back to a regular pumper, Squad 2 had the infamous FrankenSquad.