The point about the words 'regular' and 'irregular' is that the regular verbs follow a regular pattern. Unless students are told that a verb is not regular then they know the patterns for the overwhelming majority of existing verbs and for all new verbs::
verb - verbs/verbing/(have) verbed
verbe - verbes/verb(e)ing/ (have) verbed
bie - bies/bying/(have) bied
verby - verbies/verbying/(have) verbied
verch - verches/verching/(have) verched
veb - vebs/vebbing/(have) vebbed
verber - verbers/verbering/(have verbered)
verber - verbers/verberring/(have) vererred
Verbs such as spell that have two forms are conveniently presented as having a regular and an irregular form.
Verbs that do not follow regular patterns are conveniently referred to as 'irregular'. If students meet an unknown irregular verb krake, they have no idea whether it follows the pattern of awake, make or take - or something different.
The idea of strong and weak verbs is not helpful in modern English. Your 'strong verbs' may be ancient and natural, but they are certainly not regular.