I wonder if it is possible to replace the original firmware with some other linux i.e. NanoNAS or MINT?
Yes, theoretically. Here
is a story about putting Debian on that nas. Unfortunately you're stick to that old kernel (the Oxnas 810 is not supported by the Vanilla kernel) so a modern distro is impossible. In the Iomega HMNHD subforum you can find info about upgrading the provided Debian Lenny to Squeeze, (you need to keep Lenny udev), but Wheezy won't work.
Unfortunately, I'm disappointed with my NAS221 and providing I'm incapable of fixing it in a normal way round, I will switch to x86 based NSA.
An x86 based nas is not necessarily easier. The examples I have seen also booted from flash, using u-boot. So installing another distro is not as simple as on a PC. At least one of them had an uncommon nic, so I don't know if you could easily upgrade the kernel. Basically putting you in the same deadended street.
An x86 based nas has more power, but it also uses more power.