You should be able to set up a Samba Server on the Raspberry Pi which would be able to host your content to the other computers on your network.
You should only need to make minimal changes to the /etc/samba/smb.conf in order to set up network shares. According to this source the default config looks like the following:
[global]
workgroup = WORKGROUP
usershare allow guests = yes
security=share
follow symlinks = yes
wide links = yes
unix extensions = no
[pi]
browsable = yes
read only = no
guest ok = yes
path = /home/pi
force user = pi
[devices]
browsable = yes
read only = no
guest ok = yes
path = /media
force user = root
If you want to create a new share, just create a new section following the format for [pi] or [devices] and changing the path to point to the directory containing your files. When you get it set up you will notice that the share name will be the same as the section name.
Heres a link to the Pi forms with people discussing the same setup.