This isn't a VirtualBox (or Windows XP) problem - you need to instruct Chrome OS to use a proxy. The virtual adapter in VirtualBox can be configured to Bridged or NAT, though NAT would probably simplify your life somewhat.
I don't have a Chrome OS VM - so this part is just a guess based on my Chrome browser, but can you click on the wrench icon -> Options -> Under The Hood (tab) -> The under the network section, click the "change proxy settings" button?
There may also be a way to export the right environment variables (http_proxy most likley) in your startup scripts, as Chrome OS shares a certain legacy with Linux and Ubuntu, but I can't comment specifically on it.
Side Note: Your VirtualBox version is a bit out-dated, have you considered upgrading?
Because the service is not accessible when the virtual nic is in either bridged mode, or is in NAT mode with a correctly configured forward rule, the issue is likely to be with the guest server, or the service itself.
Many services are not configured to accept remote connections by default, and open network ports for listening on the loop back network interface only. To determine what interface your service is bound to, use this command:
Linux:
# netstat -ntlup | grep portnumber
windows:
netstat -abno | FINDSTR LISTENING
and make note of the IP address the port/process is bound to.
# netstat -ntlup | grep 53
tcp 0 0 127.0.1.1:53 0.0.0.0:* LISTEN 835/dnsmasq
udp 0 0 127.0.1.1:53 0.0.0.0:* 835/dnsmasq
shows the dnsmasq service running on the loopback interface (127.0.x.y), and can only be accessed by processes running on the localhost.
# netstat -ntlup | grep 445
tcp 0 0 0.0.0.0:445 0.0.0.0:* LISTEN 566/smbd
tcp6 0 0 :::445 :::* LISTEN 566/smbd
However shows the service listening on ALL interfaces (0.0.0.0).
finally,
# netstat -ntlup | grep 138
udp 0 0 10.0.2.255:138 0.0.0.0:* 960/nmbd
udp 0 0 10.0.2.15:138 0.0.0.0:* 960/nmbd
shows the service listening on eth0 (host IP), and any broadcasts received on eth0 (host network broadcast address ending in .255) since Samba protocols use IP broadcasts.
Each service has its own means of enabling remote connections. this is somthing that must be configured in the service itself (no OS level control), because when the service opens the port for listening, it specifies the details of what interface to bind to. Usually (in linux) it involves specifying the interface binding in the services main configuration file, and restarting the service. In Windows, you are more likely to find a checkbox saying "allow remote connections" or some such, but you usually still have to restart the service for the change to take effect.
Best Answer
The solution would be to set the VirtualBox Proxy settings, which you can find under Preferences -> Proxy, see screenshot:
EDIT: just noticed the part about SOCKS or HTTPS proxy chains. So might not work as you want. Let us know.