No, they aren't irregular forms. The verb belongs to the first conjugation (in -are), the same as amare
The only difference is the presence of the i, which is just an orthographic device for telling the palatal pronunciation of the preceding (geminated) g. So this is a very different situation than cambiare, where there is an i in the root of the verb. However, the final realization is the same: in both cases the desinence remains -iamo; in both cases the i in the desinence is absorbed: it's not really heard in viaggiamo and it's not doubled in cambiamo.
It's a general rule in Italian that pairs of non-tonic identical vowels contract to a single one: the plural of olio is oli and, similarly, any desinence starting with i is absorbed:
cambi (not cambii)
cambiamo (not cambiiano)
In the case of viaggiare, the “purely orthographic” i is removed when there is one in the desinence, which avoids any doubt in the pronunciation: so tu viaggi and noi viaggiamo.
Somebody supports writing plurals of words ending in the diphthong -io with a double i. Somebody disagrees. But viaggio doesn't end with a diphthong, so there should be no doubt that the graphic i is dropped when it doesn't serve its purpose any more because a phonetic i is present.