You can use tools like auditd
or pspy64
to monitor activies inside your system, from the running processes. Also, you could monitor your network activity with more advanced techniques using tshark
, wireshark
or tcpdump
. You can also just check with what servers you're connected to using netstat
.
Give it a go and check if you find something useful. You could also upload those suspicious files to VirusTotal and check if they're actually malware and get some more detailed information from those.