Using LIKE in an Oracle IN clause

What would be useful here would be a LIKE ANY predicate as is available in PostgreSQL

SELECT * 
FROM tbl
WHERE my_col LIKE ANY (ARRAY['%val1%', '%val2%', '%val3%', ...])

Unfortunately, that syntax is not available in Oracle. You can expand the quantified comparison predicate using OR, however:

SELECT * 
FROM tbl
WHERE my_col LIKE '%val1%' OR my_col LIKE '%val2%' OR my_col LIKE '%val3%', ...

Or alternatively, create a semi join using an EXISTS predicate and an auxiliary array data structure (see this question for details):

SELECT *
FROM tbl t
WHERE EXISTS (
  SELECT 1
  -- Alternatively, store those values in a temp table:
  FROM TABLE (sys.ora_mining_varchar2_nt('%val1%', '%val2%', '%val3%'/*, ...*/))
  WHERE t.my_col LIKE column_value
)

For true full-text search, you might want to look at Oracle Text: http://www.oracle.com/technetwork/database/enterprise-edition/index-098492.html

No, you cannot do this. The values in the IN clause must be exact matches. You could modify the select thusly:

SELECT *
  FROM tbl
 WHERE my_col LIKE %val1%
    OR my_col LIKE %val2%
    OR my_col LIKE %val3%
 ...

If the val1, val2, val3... are similar enough, you might be able to use regular expressions in the REGEXP_LIKE operator.