I can't believe that there is no built in way in Mathematica to do this right.

It's possible to convert forth and back to character code, but then there is the problem, that the order of lists is undefined

In[32]:= {40, 43, 51, 107, 45, 49, 44, 45, 52, 110, 47, 51, 45, 51, 
  109, 43, 107, 45, 55, 47, 51, 41} > {40, 43, 51, 107, 43, 49, 44, 
  45, 110, 45, 109, 43, 107, 41}

Out[32]= {40, 43, 51, 107, 45, 49, 44, 45, 52, 110, 47, 51, 45, 51, 
  109, 43, 107, 45, 55, 47, 51, 41} > {40, 43, 51, 107, 43, 49, 44, 
  45, 110, 45, 109, 43, 107, 41}

so let's do something simple minded

In[36]:= Clear[weitzerOrder]
weitzerOrder[l1_List?VectorQ, l2_List?VectorQ] := 
 Block[{o = 1, len1 = Length[l1], len2 = Length[l2]}, 
  While[l1[[o]] == l2[[o]] && o <= Min[len1, len2], o++];
  If[l1[[o]] < l2[[o]],
   True, (* else *)
   If[o > len1,
    True, (* else *)
    False
    ]
   ]
  ]
FromCharacterCode /@ 
 Sort[ToCharacterCode /@ {"(+3k-1,-4n/3-3m+k-7/3)", "(+3k+1,-n-m+k)", "(+3k-1,-n-m+k-1)"}, weitzerOrder[#1, #2] &]

Out[38]= {"(+3k+1,-n-m+k)", "(+3k-1,-4n/3-3m+k-7/3)", "(+3k-1,-n-m+k-1)"}

But the test fails despite Sort works (anti-konform to the character code)

In[1]:= "+" < "-"
Out[1]= "+" < "-"

In[2]:= {"+"} < {"-"}
Out[2]= {"+"} < {"-"}

In[8]:= ToCharacterCode["+"] < ToCharacterCode["-"]
Out[8]= {43} < {45}

In[12]:= weitzerOrder[ToCharacterCode["+"], ToCharacterCode["-"]]
Out[12]= True

To get these in ASCII order, you will have to write your own function.

In[18]:= Clear[WRule]
WRule = {"-" -> "WMinus", "+" -> "WPlus"};
StringReplace[
   Sort[StringReplace[{"(+3k-1,-4n/3-3m+k-7/3)", "(+3k+1,-n-m+k)", "(+3k-1,-n-m+k-1)"}, WRule], OrderedQ[{#1, #2}] &], 
   Reverse /@ WRule]

Out[20]= {"(+3k-1,-4n/3-3m+k-7/3)", "(+3k-1,-n-m+k-1)", "(+3k+1,-n-m+k)"}

or if the minus should appear later

In[21]:= Clear[WRule]
WRule = {"-" -> "WLast", "+" -> "WFirst"};
StringReplace[
 Sort[StringReplace[{"(+3k-1,-4n/3-3m+k-7/3)", "(+3k+1,-n-m+k)", "(+3k-1,-n-m+k-1)"}, WRule], OrderedQ[{#1, #2}] &], 
 Reverse /@ WRule]

Out[23]= {"(+3k+1,-n-m+k)", "(+3k-1,-4n/3-3m+k-7/3)", "(+3k-1,-n-m+k-1)"}