How to use grep to search for a pattern which starts with a hyphen (-)?

sudo find / -name "*" | xargs grep -sn --color=auto "-j"

Above command returns below:

grep: invalid option -- 'j'
Usage: grep [OPTION]... PATTERN [FILE]...
Try `grep --help' for more information.
...

How do I search for string -j?

In your case "-j" is interpreted by grep as an argument/option, not as a search pattern, even if you quoted it. To make it to be the pattern for what you want to search, just use -eoption:

sudo find / -name "*" | xargs grep -sn --color=auto -e "-j"

or even:

sudo find / -name "*" | xargs grep -sn --color=auto -e -j

The -e argument/option means that the next argument is the pattern. This is from man grep:

   -e PATTERN, --regexp=PATTERN
          Use  PATTERN  as  the  pattern.   This  can  be  used to specify
          multiple search patterns, or to protect a pattern beginning with
          a hyphen (-).  (-e is specified by POSIX.)

Other ways:

• use --, as @Rinzwind said in his answer, to make grep to hnow that the options ended.

• use \ to escape the hyphen (-):

  sudo find / -name "*" | xargs grep -sn --color=auto "\-j"
  

Tell it that the options ended with --:

sudo find / -name "*" | xargs grep -sn --color=auto -- "-j"

Result:

Binary file /initrd.img matches
Binary file /lib/modules/2.6.24-16-server/ubuntu/media/gspcav1/gspca.ko matches
Binary file /lib/modules/2.6.24-16-server/ubuntu/sound/alsa-driver/isa/es1688/snd-es1688.ko matches
Binary file /lib/modules/2.6.24-16-server/ubuntu/sound/alsa-driver/pci/ice1712/snd-ice1712.ko matches
/lib/modules/2.6.24-16-server/modules.dep:1807:/lib/modules/2.6.24-16-server/kernel/fs/nls/nls_euc-jp.ko:
Binary file /lib/modules/2.6.24-16-server/kernel/crypto/blowfish.ko matches
Binary file /lib/modules/2.6.24-16-server/kernel/fs/nls/nls_euc-jp.ko matches
Binary file /lib/modules/2.6.24-16-server/kernel/fs/nls/nls_cp936.ko matches

You can escape - character using \

$ sudo find / -name "*" | xargs grep -sn --color=auto "\-j"

Also you may want to exclude folders and search only files, add -type f to find:

$ sudo find / -name "*" -type f | xargs grep -sn --color=auto "\-j"

Also if you add -P 4 to xargs, it will parallel all execution on 4 processes, and search may be done faster if you have more than 1 cores.

$ sudo find / -name "*" -type f | xargs -P 4 grep -sn --color=auto "\-j"