127.0.0.1 is a local loopback address for the machine itself. You will likely always see that one.
The 10.0.0.205 is most likely your private IP assigned via DHCP from router or static and most likely the Address that your public NATs to, if all is working
169.254.x.x is an APIPA address. Usually means an adapter tried to contact a DHCP server but was unable to. These are likely different network interfaces than the 10.0.0.205 address. Do you have multiple network cards in this machine, including wireless or virtual ones from like a VPN adapter or hardwire and wireless? Does this machine have any VMS or is it itself a virtual machine inside another host?