Well, I visited the mysql.com forums and got an answer. I thought I would post it here if it might help someone else:
First of all this method DOES NOT DELETE ANYTHING IF THERE IS MISSING DATA IN LOWER TABLES:
delete job, forms, parts
from user, job, forms, parts
where user.user = 14 and
job.job in (1,3) and
user.user = job.user and
user.user = forms.user and
user.user = parts.user and
job.job = forms.job and
job.job = parts.job and
forms.forms = parts.forms;
However this method DOES DELETE ALL APPLICABLE RECORDS EVEN IF THERE IS MISSING DATA IN LOWER TABLES:
DELETE job, forms, parts
FROM user
LEFT JOIN job ON job.user = user.user
LEFT JOIN forms ON forms.user = user.user AND forms.job = job.job
LEFT JOIN parts ON parts.user = user.user AND parts.job = job.job AND parts.forms = forms.forms
WHERE user.user = 14 AND job.job in (1,3);