Working with text in 3D graphics

You could always just Texture your Text in:

o = Graphics3D[{{EdgeForm[{Thickness[.000001], GrayLevel@0}], Blue, 
 Cuboid[{-4, 0, 0}, {4, 2.4, 1}]}, {EdgeForm[{Thickness[.000001], 
   GrayLevel@0}], Blue, 
 Cuboid[{-4, 3.4, 0}, {4, 3.6, 
   1}]}, {EdgeForm[{Thickness[.000001], GrayLevel@0}], Blue, 
 Cuboid[{-4, 4.6, 0}, {4, 7, 1}]}, {EdgeForm[{Thickness[.000001], 
   GrayLevel@0}], Blue, Cuboid[{-4, 0, 0}, {4, 7, -1}]}, {Cyan, 
 Opacity[.95], Cuboid[{-4, 2.4, 0}, {4, 3.4, 1}]}, {Yellow, 
 Opacity[.95], Cuboid[{-4, 3.6, 0}, {4, 4.6, 1}]}}, Boxed -> False, 
 ImageSize -> 800];

text = First[
   First[ImportString[
     ExportString[
      Style["testing one two three", Italic, FontSize -> 24, 
       FontFamily -> "Times"], "PDF"], "PDF", 
     "TextMode" -> "Outlines"]]];
r = ImagePad[
   Rasterize[Graphics[{EdgeForm[None], Darker@Blue, text}], 
    Background -> None, 
    ImageResolution -> 1000], {{200, 200}, {0, 30}}];
face = {{-4, 2.4`, 1.01`}, {4, 2.4`, 1.01`}, {4, 3.4`, 1.01`}, {-4, 
    3.4`, 1.01`}};
Show[o, Graphics3D[{Texture[r], 
   Polygon[RotateRight[face, 4], 
    VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}], 
 Lighting -> "Neutral"]

Like M.R. I recommend using texture mapping to put a label on a surface. However, I would write somewhat simpler code to do it.

First rasterize the text.

text =
  Rasterize[Style["Text as a texture", "SR"],
    RasterSize -> 500, ImageSize -> 200, Background -> None];

Next make a 3D-polygon having the rasterized text mapped onto it. The polygon is is designed to float just above the cuboid surface it labels.

label =
  With[
    {rectangle =
       With[{dz = .001}, 
         {{-4, 3.6, 1 + dz}, {4, 3.6, 1 + dz}, {4, 4.6, 1 + dz}, {-4, 4.6, 1 + dz}}],
     textCorners = {{0, 0}, {1, 0}, {1, 1}, {0, 1}}},
    {Texture[text], Polygon[rectangle, VertexTextureCoordinates -> textCorners]}];

Finally, add the label to your graphics.

Graphics3D[
  {{Blue, EdgeForm[],
     {Cuboid[{-4, 0, 0}, {4, 2.4, 1}], 
      Cuboid[{-4, 3.4, 0}, {4, 3.6, 1}], 
      Cuboid[{-4, 4.6, 0}, {4, 7, 1}], 
      Cuboid[{-4, 0, 0}, {4, 7, -1}]}}, 
   {Cyan, Cuboid[{-4, 2.4, 0}, {4, 3.4, 1}]}, 
   {Yellow, Cuboid[{-4, 3.6, 0}, {4, 4.6, 1}]},
   label},
  Boxed -> False, ImageSize -> 500] 

An approach without using Texture:

1. Use M.R.'s ImportString[ExportString[..., "PDF"], "PDF", "TextMode" -> "Outlines"] trick to make your text into a list of FilledCurves.
2. Use the function filledCurveToPolygons3D this answer by Simon Woods to convert FilledCurves to polygons in 3D
3. Use NDSolve`FEM`GraphicsPrimitiveToGraphicsComplex to convert graphics primitives to GraphicsComplex
4. Use the function rescale below to Rescale the coordinates of the primitives from the previous step to place them in the appropriate positions in the input Graphics3D.

Using text and o from @M.R.'s answer:

gc3d = NDSolve`FEM`GraphicsPrimitiveToGraphicsComplex[Cases[text /. 
     f_FilledCurve :> filledCurveToPolygons3D[f], _Polygon, Infinity]];

rescale[ranges_, style___ : FaceForm[Red]] := # /. 
    GraphicsComplex[c_, prims___] :>  GraphicsComplex[
      Transpose[Table[Rescale[Transpose[c][[i]], 
         Through[{Min, Max}@Transpose[c][[i]]], ranges[[i]]], {i, 1, 3}]], 
     {style, prims}] &;

ranges1 = {{-3.6, 3.6}, {2.5, 3.3}, {1.001, 1.001}};
ranges2 = {{-3.6, 3.6}, {3.5, 4.5}, {1.001, 1.001}}
ranges3 = {{3.6, -3.6}, {6.5, 5}, {1.001, 1.001}};
Show[Graphics3D[rescale[ranges1] @ gc3d], 
 Graphics3D[rescale[ranges2, EdgeForm[], FaceForm[Blue]] @ gc3d], 
 Graphics3D[rescale[ranges3, EdgeForm[], FaceForm[Yellow]] @ gc3d], o]