How secure are my locks?

Python, 253 246 bytes

m=lambda a,b:min(sorted(a),sorted(b))
def w(s):
    if type(s)!=list:return[s]
    if len(s)==1:return s
    k=w(s[0])
    z=w(s[2])
    if s[1]=="|":return m(k,z)
    return k+z
r=[]
for i in n:r+=[(i,sorted(w(i),reverse=1))]
sorted(r,reverse=1,key=lambda x:x[1])

Perl 6: 132 124 bytes

{reverse .sort: {use MONKEY-SEE-NO-EVAL;my &infix:<|>={|$^a,|$^b}
min map *.flat.sort.squish.reverse,EVAL .trans('&'=>'X')}}

A lambda that takes a list of lines as input.

It generates the sort key for each line as follows:

• Declare | as a list concatenation operator within the lexical scope.
• Replace & in the string with X, the Perl 6 cartesian product operator.
• Eval the string (which unfortunately requires the ghastly MONKEY-SEE-NO-EVAL pragma), yielding all possible combinations of keys that open the door.
• Post-process the lists and pick the "least secure" combination.