There are a couple syntax errors in your code. I would not recommend assigning a set of equations to a variable and then passing that variable into an NDSolve or DSolve. Additionally the constants that are present in your differential equations do not have a common notation -- i.e. p[6] instead of p6. And I cannot see that p6 is called in your set of equations. Is that meant to be the case? From a theoretical perspective, you should be looking for analytic solutions before brute numerical solutions. Have you tried that?

A cleaner version of the code to search for analytic solutions might look like:

      p1 = 50;
      p2 = 70.5;
      p3 = .16;
      p5 = 1600;
      p6 = .05;
      p7 = 0.03;
      sol1 = DSolve[{s'[t] == -p3 (r[t] s[t] c[t]/(p1*p2))/((1 + s[t]/p1) (1 + c[t]/p2)) , 
      w'[t] ==p3*p5 (r[t] s[t] c[t]/(p2*p2))/((1 + s[t]/p2) (1 +c[t]/p3)) - 
      w[t], c[t] == -(1 + p1/s[t]) (r[t]*s[t]*
     c[t]/(p1*p2))/((1 + s[t]/p1) (1 + c[t]/p2)) - 
 p7*c[t] r[t] == -p7*r[t], s[0] == 150, w[0] == 0, c[0] == 0.05, 

r[0] == 0.05}, {s[t], w[t], c[t], r[t]}, {t}]

To look for numerical solutions, a cleaner version of the last section of the code might look like:

sol = NDSolve[{s'[
  t] == -p3 (r[t] s[
      t] c[t]/(p1*p2))/((1 + s[t]/p1) (1 + c[t]/p2)) w'[t], 
w'[t] == 
 p3*p5 (r[t] s[t] c[t]/(p2*p2))/((1 + s[t]/p2) (1 + c[t]/p3)) - 
  w[t], c[t] == -(1 + p1/s[t]) (r[t]*s[t]*
      c[t]/(p1*p2))/((1 + s[t]/p1) (1 + c[t]/p2)) - 
  p7*c[t] r[t] == -p7*r[t], s[0] == 150, w[0] == 0} /. {p1 -> 50, 
p2 -> 70.5, p3 -> .16, p5 -> 1600, p[6] -> .05, p7 -> 0.03}, {s, 
 w, c, r}, {t, 0, 120}]

Attachments:

Your deq4 looks like deq4 := r[t] == -p[7] r[t]; This says that -p[7] is one? But you later on write p[7] -> 0.003

It will be better to post the actual code here than attaching a notebook. The code is not large.

I also do not know why you used indexed variables p[3] etc.. instead of normal variables p3 etc.... There is no need at all to use indexed variable instead of normal variables. Having [] all over the code makes it hard to read.

I would also like to suggest not to use l for variable name, as it looks like a 1 on many screen and fonts. The error you get indicates an inconsistent initial condition. Please see NDSolveIntroductoryTutorialDAEs