How to cat multiple lines with indentation in bash function?

Either use tabs and <<-EOF (with the dash) or use a filter instead of cat, eg. sed:

$ sed -e "s/^\s*//" <<EOF
 as
  df
   gh
    jk
        op    # two tabs
EOF

This removes both spaces and tabs. Note that the closing EOF cannot be indented. You might use <<" EOF" and then the again " EOF" with the same number of spaces as the end token, but the quotes block the expansions in the here-document, which you don't want in this case. Compare:

$ a=x
$ cat <<EOF
"$a"
EOF
"x"
$ cat <<"EOF"
"$a"
EOF
"$a"

As for echo it has problems with this. But you can use printf also:

printf "%s\n" \
  "[influxdb]" \
  "name = InfluxDB Repository - RHEL \$releasever" \
  "baseurl = https://repos.influxdata.com/rhel/\$releasever/\$basearch/stable" \
  "enabled = 1" \
  "gpgcheck = 1" \
  "gpgkey = https://repos.influxdata.com/influxdb.key" \
| sudo tee /etc/yum.repos.d/influxdb.repo

I left the dashes in \$ as in your question, but they may not be correct here, as they're escaping the expansions.

You need to use <<- (note the -) which specifically enables what you want.

yumtelegraf() {
  cat <<-EOF | sudo tee /etc/yum.repos.d/influxdb.repo
  [influxdb]
  name = InfluxDB Repository - RHEL \$releasever
  baseurl = 
  https://repos.influxdata.com/rhel/\$releasever/\$basearch/stable
  enabled = 1
  gpgcheck = 1
  gpgkey = https://repos.influxdata.com/influxdb.key
  EOF
  sudo yum install telegraf
}

You can use echo -e "\tblabla":

$ echo -e "\tblabla\n\t\tblibli\n\t\t\tbloblo\n"
    blabla
        blibli
            bloblo

As explained in bash manual page:

If the -e option is given, interpretation of the following backslash-escaped characters is enabled.
[...]
              \a     alert (bell)
              \b     backspace
              \c     suppress further output
              \e
              \E     an escape character
              \f     form feed
              \n     new line
              \r     carriage return
              \t     horizontal tab
              \v     vertical tab
              \\     backslash
              \0nnn  the eight-bit character whose value is the octal value nnn (zero to three octal digits)
              \xHH   the eight-bit character whose value is the hexadecimal value HH (one or two hex digits)
              \uHHHH the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHH (one to four hex digits)
              \UHHHHHHHH
                     the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHHHHHH (one to eight hex digits)