How to make a Slash header in Grid?

You might want to try something like this:

Grid[
 Transpose@
  Insert[
   Transpose@
    Insert[
     Table[
      aaa,
      {ab, {{1, 1}, {1, 2}, {1, 3}, {2, 3}}}, {\[Phi], {0, \[Pi]/
         4, \[Pi]/2, (3 \[Pi])/4, \[Pi]}}], {0, \[Pi]/4, \[Pi]/
       2, (3 \[Pi])/4, \[Pi]}, 1
     ],
   {
    Graphics[{
      Line[{{0, 1}, {2, 0}}],
      Text[Style["x:y", "StandardForm", Larger], {0.5, 0.25}],
      Text[Style["\[Phi]", "StandardForm", Larger], {1.5, 0.75}]
      },
     ImageSize -> Tiny],
    "1:1", "1:2", "1:3", "2:3"}, 1],
 Frame -> All
 ]

It's probably not the most robust solution in terms of scaling/spacing, but I think it comes close to what you wanted to achieve.

There's Backslash:

Grid[Transpose@
  Insert[Transpose@
    Insert[Table[
      aaa,
      {ab, {{1, 1}, {1, 2}, {1, 3}, {2, 3}}},
      {ϕ, {0, π/ 4, π/2, (3 π)/4, π}}],
    {0, π/4, π/2, (3 π)/4, π}, 1],
   {Backslash["x:y", ϕ], "1:1", "1:2", "1:3", "2:3"}, 1],
 Frame -> All]

You can use various things to control size and placement. For instance, using

Backslash[Pane["x:y", ImageSize -> {Automatic, 30}, Alignment -> Bottom], ϕ]

results in

Update

This looks a little better to me, but one can spend a lot of time fussing just to satisfy one's picayune aesthetic quirks.

Grid[Transpose@
  Insert[Transpose@
    Insert[Table[
      aaa,
      {ab, {{1, 1}, {1, 2}, {1, 3}, {2, 3}}},
      {ϕ, {0, π/ 4, π/2, (3 π)/4, π}}],
    {0, π/4, π/2, (3 π)/4, π}, 1],
  {Backslash["x:y", Pane[ϕ, ImageSize -> {Automatic, 30}, Alignment -> Center]],
     "1:1", "1:2", "1:3", "2:3"}, 1], Frame -> All, 
 Alignment -> {Center, Center, Table[{i, 1} -> ":", {i, 5}]}]