Nope. It's viruses. That issue has been discussed many times on the
virus newsgroups by language experts.
The correct English plural of virus is viruses. Please consult any good
dictionary before making up words.
For the purists, in Latin, there is a rarely-used plural form:
virus, viri (neuter)
(Forms: almost always restricted to nominative and accusative singular;
generally singular in Lucretius, ablative singular in Lucretius)
The point of this is that even in Latin the form "viri" is rarely used.
The singular form is used in most every instance. (This is from the
Oxford Latin Dictionary.)
So, when considering the Latin: "virii" is incorrect and "viri" was
almost never used.
Despite the fact there was little use for the plural form, there is
another reason why "viri" was rarely used. The most common Latin word
for "man" is "vir" with "viri" being its plural in the form used as the
subject of a sentence. Thus, since "men" as the subject of a sentence
would be used far more often than "venoms" (virus means venom) the
"viri" word was most commonly seen as the plural of "man."
Bottom line: Don't try to make up words using a false Latin plural form.
Since the word virus in its English form is now used then the English
plural (viruses) should be used.