How to use package classes and call packages from Oracle11gr2 stored procedure in certain schema

Best practice is always qualify schema for all object references. See this by Tibor Karaszi or this by Midnight DBA or just trust me or the MS SQL Server Best Practice Analyzer

But you can run this if you choose to ignore best practice:

ALTER SCHEMA dbo TRANSFER John.mySP_Name;

There is great reason why you should never call stored procedures from within triggers.

Triggers are, by nature, stored procedures. Their actions are virtually hard to roll back. Even if all underlying tables are InnoDB, you will experience a proportional volume of shared row locks and annoying intermittency from exclusive row locks. Such would be the case if triggers were manipulating tables with INSERTs and UPDATEs being stagnated to perform heavy duty MVCC inside each call to a trigger.

Don't forget that Triggers require overhead. In fact, According to MySQL Stored Procedure Programming, page 256 under the head "Trigger Overhead" says the following:

It is important to remember that, by necessity, triggers add overhead to the DML statement to which they apply. the actual amount of overhead will depend upon the nature of the trigger, but --- as all MySQL triggers execute FOR EACH ROW --- the overhead can rapidly accumulate for statements that process large numbers of rows. You should therefore avoid placing any expensive SQL statements or procedural code in triggers.

An expanded explanation of trigger overhead is given on pages 529-531. The concluding point from that section states the following:

The lesson here is this: since the trigger code will execute once for every row affected by a DML statement, the trigger can easily become the most significant factor in DML performance. Code inside the trigger body needs to be as lightweight as possible and -- in particular -- any SQL statements in the trigger should be supported by indexes whenever possible.

I explained other nasty aspects of Triggers in an earlier post.

SUMMARY

I would strongly recommend not calling any stored procedures from a Trigger, even if MySQL allows it. You should wlays check out the current restrictions for MySQL 5.5.