Well, assuming that you insist on keeping it in ternary form for whatever reason, your readability would go up considerably if you'd just format it correctly.
const bool cond1 = MEMWBRegWrite && MEMWBrd != 0 &&
!(EXMEMRegWrite == 1 && EXMEMrd != 0 && EXMEMrd == IDEXrs) &&
MEMWBrd == IDEXrs;
ForwardA = cond1
? 2'b01
: ((EXMEMRegWrite && EXMEMrd != 0 && EXMEMrd == IDEXrs) ? 2'b10 : 0);
const bool cond2 = IDEXTest == 0 &&
MEMWBRegWrite && MEMWBrd != 0 &&
!(EXMEMRegWrite == 1 && EXMEMrd != 0 && EXMEMrd == IDEXrt) &&
MEMWBrd == IDEXrs;
ForwardB = cond2
? 2'b01
: ((EXMEMRegWrite && EXMEMrd != 0 && EXMEMrd == IDEXrt && IDEXTest == 0) ? 2'b10 : 0);
Now, that code is formatted as if it were C++ rather than whatever you're actually using, but it becomes much easier to figure out what's going on.
However, I would point out that your if-statements can't possibly match your ternary expressions. Your if statements have no else clause, and ternary expressions always have else clauses. However, since your question doesn't even make it entirely clear whether you're trying to convert the if-statements into ternary expressions or the ternary expressions into if-statements, it's a bit hard to give you exactly what you want.
EDIT: Ternary expressions always have both an if and an else clause. You cannot directly turn an if statement without an else clause into a ternary because you wouldn't have the else portion of the ternary. Now, you can pull some tricks in some cases if you need to, like setting a variable to itself. For instance,
ForwardA = cond1 ? newValue : FordwardA;
You're basically saying not to change the value in the else clause - but that's assuming that you're assigning the result to a variable. The more complicated the expression, the harder it is to pull that sort of trick, and the more convoluted the code becomes when you do. Not to mention, depending on what optimizations that the compiler does or doesn't do, it could be assigning the variable to itself, which isn't terribly efficient.
Generally-speaking, translating if-statements with no else clauses into ternary expressions is a bad idea. It can only be done by pulling tricks rather than directly saying what you mean, and it just complicates things. And this code is complicated enough as it is.
I'd advise not using a ternary here unless you really need it. And if you do, at least break down the expression. Even if your ternary expression were correct, it's much harder to read than the if-statements.
EDIT 2: If you really do need this to be a ternary expression, then I'd advise that you sit down and figure out the exact conditions under which ForwardA should be what set of values and create a ternary expression based on that rather than trying to directly convert the if-statements that you have (and the same for ForwardB). Your if-statments are not only deciding what value to assign to each variable, but which variable to assign that value to, and that complicates things considerably.
In other languages (I don't know about verilog), you can use a ternary expression for choosing which variable to assign the value to in addition to whatever you're doing on the right side of the expression, but that's getting really complicated. It might be best to create a temporary which holds the value which is to be assigned and a separate ternary to determine which variable to assign it to.
Not knowing verilog, I really don't know what you can and can't do with if-statements and ternary expression, but I would think that there's got to be a better way to handle this than using a ternary. Maybe not, but what you're trying to do is very difficult and error-prone.