Let'say I have a device with a camera, and this device should stream the video data to a server. I want to prevent people connected on the same network of the camera to eavesdropping on my video stream. If I setup a VPN client on the device and a VPN server on my server, can I be able to prevent succesfully eavesdropping on my unencrypted video stream?
Yes, a VPN will secure the connection between the camera device and the server. If its only for the RTSP (or similar) stream, then a SSL tunnel would also suffice and gives less overhead, and is easier to configure.
Yes a VPN creates a secure tunnel thereby stopping people in your network from eaves dropping. You can make your own VPN or use a service. I've created my very own VPN for Raspberry Pi where I've create my own server connection. But on Windows and Android I use Ivacy VPN Apps instead if manually configuring the VPN.