We have a bunch of DL-380 G6 servers in our company, I want to know whether it is possible to use 2.5" SSD hard drives (with SATA III interface) on these servers or not?
No, you can't just use any SSD in that model server.
The Smart Array P410 array controller is a little sensitive, but will work with most SSDs. For others, it may not recognize the disks or will show error lights or even cause the system fan speeds to increase (because of misread SSD temperature sensors).
Being more specific about which SSDs you'd like to use would be helpful.
But another consideration is that SATA disks on that controller will be downshifted to 3.0Gbps speeds instead of 6.0Gbps. Also, the controller has an IOPS limit of ~50,000, so there's a performance ceiling of ~6 disks.
Please see: Samsung 850 EVO + HP P410 limited iops?