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grep 'string1\|string2\|string3' filename

I would like to clarify, you can't use inbuilt commands. You have to actually implement the grep function, also the strings can be part of words in the file.

correction not sentences but lines

Can this be treated as a set intersection problem?
Create sets of lines which contains string1. Similarly for string2 and string3.
The solution would be to union of all the three sets.

The question then would be how to create sets for these strings? I mean, should it be line number or the entire line itself that should go in the sets?

this problem is solved by using strstr in built c function...

first intialize the variable str1,atr2,str3 with the given input string
and take one buf[maxsize]; int i=0;
file* fp= fopen(argv[1],"r");
while(ch!=null){
ch=fread(fp,1,1);
buff[i]=ch;
if(ch=='\n'){if((strstr(buf,str1))!==null) printf("%s",buf);
if((strstr(buf,str2))!==null) printf("%s",buf);
if((strstr(buf,str1))!==null) printf("%s",buf);

i=0;
}
else
{ i++
}

}

We can use Hash code for the above problem... For the 3 strings we can calculate Hash code and we can store it.... then we can start reading the file, and we will calculate the Hash code for each word and if it matches with any 3 string hash code, we will print the entire line and then the same process is repeated for the next line and so on..

would it be better to just use normal string comparison using strcmp rather than creating a hash code and again matching the hash code??

First off.. lets just use a fast string compare algorithm... we can easily use Knuth Morris Pratt.
Start string matching with the first word.
For each sentence first just try out the entire sentence for the first word. If there is a match, print the sentence and go to the next. If there is no match, repeat the search on the sentence with the next word and so on...
That way.. if we get a match.. we print the sentence.. and we dont need to test the sentence again with another word because it is redundant.