If you use a cell array, that'll require cellfun
> isOK=~cellfun(@isempty,strfind(C(:,1),'Normal')) & [[C{:,2}]>=20].';
>> C(isOK,:)
ans =
'Normal' [24]
'Normal' [23]
>>
Other is just the complement of ~isOK of course.
This would be far easier to write if you would use a table and categorical variables.
NB: here I presumed the second cell is numeric not string...if were another string have to "wash, rinse, repeat" the strfind operation for each.
regexp is a little more friendly with cell strings but as noted, the table class and categorical variables are very useful for such data.
