You can organize your conditions already inside Which

Which[j == jp == 0 && \[Lambda]w == \[Lambda]wp == 
   0 && \[Lambda]1 + \[Lambda]2 == \[Lambda]w, Red,
 j == jp == 1 && \[Lambda]w == \[Lambda]wp == 0, Blue,
 True, Black]

or whatever you want. You may consider other conditional constructs such as If and Switch, depending on your needs. A condition can also be inserted into the replacement rule:

{Style[term_ /; condition, Red] :> (term /. H[1/2, 0] -> value1), 
 Style[term_, Blue] :> (term /. H[1/2, 0] -> value2)}

provided that the condition only depends on the term.

You can make a replacement:

{Style[term_, Red] :> (term /. H[1/2, 0] -> value1), 
 Style[term_, Blue] :> (term /. H[1/2, 0] -> value2)}

How about coloring them?

Sum[Style[((-1)^(j + jp)) h1[\[Lambda]l, 
    1/2] KroneckerDelta[\[Lambda]2 - \[Lambda]w, \[Lambda]2 - \
\[Lambda]wp]*d3[j, \[Lambda]w, \[Lambda]l - (1/2)]*
   d3[jp, \[Lambda]wp, \[Lambda]l - (1/
       2)] H[\[Lambda]2, \[Lambda]w] Conjugate[
    H[\[Lambda]2, \[Lambda]wp]], 
  Which[j == jp == 0 && \[Lambda]w == \[Lambda]wp == 0, Red, 
   j == jp == 1 && \[Lambda]w == \[Lambda]wp == 0, Blue, True, 
   Black]], {j, 0, 1}, {jp, 0, 
  1}, {\[Lambda]w, {1, 0, -1}}, {\[Lambda]wp, {1, 
   0, -1}}, {\[Lambda]l, {-1/2, 1/2}}, {\[Lambda]2, {-1/2, 1/2}}]

In the output I am getting one term 96*0 which I copied here and got following command: 96 \!(* StyleBox["0", StripOnInput->False, LineColor->GrayLevel[0], FrontFaceColor->GrayLevel[0], BackFaceColor->GrayLevel[0], GraphicsColor->GrayLevel[0], FontColor->GrayLevel[0]]) I am not able to understand this line. Why is it appearing in output ?

Thank you for your reply. This is useful for me but is there a way that with the combination of j= jp= lambdaW= lambdaWp = 0, then h[1/2,0] is defined as h[1/2,t] ? This is easily distinguishable from the other combination because it will be helpful in my further analysis if we can do in this way .