#PHP, 153 bytes

awfully long :(

for($s=$argv[$k=1];$t=$argv[++$k];){for(;$s>""&&strstr($t,$s)!=$t;$s=substr($s,0,-1))echo"$s
";for($i=strlen($s);$s<$t;$s.=$t[$i++])echo"$s
";echo"$s
";}

Run with php -nr '<ode>' <text1> <text2> ....

PHP, 153 bytes

awfully long :(

for($s=$argv[$k=1];$t=$argv[++$k];){for(;$s>""&&strstr($t,$s)!=$t;$s=substr($s,0,-1))echo"$s
";for($i=strlen($s);$s<$t;$s.=$t[$i++])echo"$s
";echo"$s
";}

Run with php -nr '<ode>' <text1> <text2> ....

#PHP, 126 bytes

for($s=$argv[1];strstr($s,$t=$argv[2])!=$t;$s=substr($s,0,-1))echo"$s
";for($i=strlen($s);$s<$t;$s.=$t[$i])echo"$s
";echo$s;

Run with -r.

#PHP, 153 bytes

awfully long :(

for($s=$argv[$k=1];$t=$argv[++$k];){for(;$s>""&&strstr($t,$s)!=$t;$s=substr($s,0,-1))echo"$s
";for($i=strlen($s);$s<$t;$s.=$t[$i++])echo"$s
";echo"$s
";}

Run with php -nr '<ode>' <text1> <text2> ....

#PHP, 111 bytes

for($s=$argv[1];strstr($s,$t=$argv[2])==$t;$s=substr($s,0,-1))echo$s;
for($i=strlen($s);$s<$t;$s.=$t[$i])echo$s;

added a linebreak for readability. Run with -r.

#PHP, 126 bytes

for($s=$argv[1];strstr($s,$t=$argv[2])!=$t;$s=substr($s,0,-1))echo"$s
";for($i=strlen($s);$s<$t;$s.=$t[$i])echo"$s
";echo$s;

Run with -r.