05AB1E, 63 61 bytes

„Uuõª„LLæDl«âDí«JéRʒÅ¿}нõ.;Ðć_ilDć'xQiA6£мÐþQë\7ÝKõQë\þQ}sõÊ*

This isn't too easy without regexes.. :/ Can definitely be golfed a bit more, though.

Try it online or verify all test cases.

Explanation:

„Uu                 # Push string "Uu"
   õª               # Convert it to a list of characters, and append an empty string:
                    #  ["U","u",""]
     „LL            # Push string "LL"
        æ           # Take its powerset: ["","L","L","LL"]
         Dl         # Create a lowercase copy: ["","l","l","ll"]
           «        # Merge the lists together: ["","L","L","LL","","l","l","ll"]
            â       # Create all possible pairs of these two lists
             Dí     # Create a copy with each pair reversed
               «    # Merge the list of pairs together
                J   # Join each pair together to a single string
                 éR # Sort it by length in descending order

We now have the list:

["llu","LLu","llU","LLU","ull","uLL","Ull","ULL","ll","LL","lu","lu","Lu","Lu","lU","lU","LU","LU","ll","LL","ul","ul","uL","uL","Ul","Ul","UL","UL","l","l","L","L","u","u","U","U","l","l","L","L","u","u","U","U","","","",""]

ʒ                   # Filter this list by:
 Å¿                 #  Where the (implicit) input ends with this string
}н                  # After the filter: only leave the first (longest) one
  õ.;               # And remove the first occurrence of this in the (implicit) input
Ð                   # Triplicate the string
 ć                  # Extract head; pop and push remainder-string and first character
                    # separated to the stack
  _i                # If this first character is a 0:
    l               #  Convert the remainder-string to lowercase
     D              #  Duplicate it
      ć             #  Extract head again
       'xQi        '#  If it's equal to "x":
           A        #   Push the lowercase alphabet
            6£      #   Only leave the first 6 characters: "abcdef"
              м     #   Remove all those characters from the string
               Ð    #   Triplicate it
                þ   #   Only keep all digits in the copy
                 Q  #   And check that the two are still the same
                    #   (thus it's a non-negative integer without decimal .0s)
          ë         #  Else:
           \        #   Discard the remainder-string
            7Ý      #   Push list [0,1,2,3,4,5,6,7]
              K     #   Remove all those digits
               õQ   #   Check what remains is an empty string
   ë                # Else:
    \               #  Discard the remainder-string
     þ              #  Only keep all digits
      Q             #  And check that the two are still the same
                    #  (thus it's a non-negative integer without decimal .0s)
   }s               # After the if-else: Swap the two values on the stack
                    # (this will get the remaining copy for "0x" cases,
                    #  or the implicit input for other cases)
     õÊ             # Check that this is NOT an empty string
       *            # And check that both are truthy
                    # (after which the result is output implicitly)