How many washbasins on how many floors?
Although this is not technically correct it may explain some thinking.
If they are all in the same position on different floors going up in a line then they may all be on the one stack. The spitting and sucking could be either syphonage or back pressure.
If the drain is blocked the trap seals will blow back, the bottom one the most probably. If the very bottom one blows then you know the blockage is somewhere either below where it joins the stack or underground. Either way you should have an access point somewhere either outside under a cover or inside at the base of the stack or even a sealed internal access cover.
Being an old building though I would check the main manhole access first and any other external access points to make sure they are clear.
If they are clear and obviously not blocked right up to the ground floor basin, then the problem could be a blocked vent.
As water is discharged into a pipe it forms something like a plug which pushes air in front of it and sucks air down the pipe behind it.
That is why if you have a blocked stack, and discharge a basin higher up the stack, the water from the basin pushes the air out, but it can't get out down the main drain if its blocked, so it pushes air and water out through the lower traps blowing their seals.
However if the vent is blocked and the water discharged can't suck air down the vent, it sucks the water seals out of the traps trying to get air that way.
We have had lovely fine weather of late and some times birds love to nest in the top of vents if there is no cage on the terminal, so nests can block the vent.
If you remove the top basin trap and let a couple of the lower basins go, you should feel the discharged water pulling in air down the top trap pipe, that is if the vent is blocked.
Please come on again if this is no use!
