Why do I get java.lang.AbstractMethodError when trying to load a blob in the db?

With JDBC, that error usually occurs because your JDBC driver implements an older version of the JDBC API than the one included in your JRE. These older versions are fine so long as you don't try and use a method that appeared in the newer API.

I'm not sure what version of JDBC setBinaryStream appeared in. It's been around for a while, I think.

Regardless, your JDBC driver version (10.2.0.4.0) is quite old, I recommend upgrading it to the version that was released with 11g (download here), and try again.

It looks that even if the driver 10.2 is compatible with the JDBC3 it may not work with JRE6as I've found here:

http://www.oracle.com/technology/tech/java/sqlj_jdbc/htdocs/jdbc_faq.html#02_03

Which JDBC drivers support which versions of Javasoft's JDK?

pre-8i OCI and THIN Drivers - JDK 1.0.x and JDK 1.1.x
8.1.5 OCI and THIN Drivers - JDK 1.0.x and JDK 1.1.x
8.1.6SDK THIN Driver - JDK 1.1.x and JDK 1.2.x (aka Java2)
8.1.6SDK OCI Driver - Only JDK 1.1.x
8.1.6 OCI and THIN Driver - JDK 1.1.x and JDK 1.2.x
8.1.7 OCI and THIN Driver - JDK 1.1.x and JDK 1.2.x
9.0.1 OCI and THIN Driver - JDK 1.1.x, JDK 1.2.x and JDK 1.3.x
9.2.0 OCI and THIN Driver - JDK 1.1.x, JDK 1.2.x, JDK 1.3.x, and JDK 1.4.x
10.1.0 OCI and THIN Driver - JDK 1.2.x, JDK 1.3.x, and JDK 1.4.x
10.2.0 OCI and THIN Driver - JDK 1.2.x, JDK 1.3.x, JDK 1.4.x, and JDK 5.0.x
11.1.0 OCI and THIN Driver - JDK 1.5.x and JDK 1.6.x

Oracle 10.2.0 supports:

Full support for JDBC 3.0
Note that there is no real change in the support for the following in the database. Allthat has changed is that some methods that previously threw SQLException now do something more reasonable instead.
result-set holdability
returning multiple result-sets.

Here's what the JDK API says about AbstractMethodError:

Thrown when an application tries to call an abstract method. Normally, this error is caught by the compiler; this error can only occur at run time if the definition of some class has incompatibly changed since the currently executing method was last compiled.

Bug in the oracle driver, maybe?