Sending RPC calls asynchronously I have ubuntu server running Bitcoin core v0.16.

I'm sending RPC calls asynchronously using Guzzle (PHP library), but, e.g., if I'm importing 1000 address using importmulti command, any further requests are waits until that command finish.

Even though I have set rpcthreads=100
rpcworkqueue=50 and I've powerful server.
importmulti is a completely blocking RPC call, no amount of CPU power or RPC threads will prevent it from being blocking. You need to create applications which do not use this command if it is an option.