Assuming the XML is well formed, such as
<?xml version="1.0" encoding="UTF-8"?>
<weblogic-service>
<service_info name="dummyapp" version="5.0"/>
<object name="WebApplications">
<item Location="dummyapp/ear/dummyapp.ear" name="dummy"/>
</object>
<object name="jdbc_oracle_nonxa">
<item db_name="MYDB1" db_user="dummyapp_user" global_trans="None" initial_size="10" jndi_name="dummyapp-aty-ds" max_size="25" name="dummyapp-aty-ds" statement_cache_size="10"/>
</object>
</weblogic-service>
(I've closed tags that were not closed in the question)
... then the following will output 25 (for this example):
xml sel -t -v '//item/@max_size' -nl file.xml
This is using XMLStarlet to get the value of the max_value attribute of all item nodes. The -nl at the end inserts a newline after the output.
If you need to be more specific and only look at the item node in the object node whose name is jdbc_oracle_nonxa:
xml sel -t -v '//object[@name="jdbc_oracle_nonxa"]/item/@max_size' -nl file.xml
Note that XMLStarlet is installed as xmlstarlet rather than xml on some systems.
Using xmllint (no newline at end of output):
xmllint --xpath 'string(//object[@name="jdbc_oracle_nonxa"]/item/@max_size)' file.xml