If you you need to convert spatial data on the fly, meaning for example you have an oracle session and need to query a table with spatial column in mysql db , you must use the Oracle Gateway for MySql [here]. Then you must use OGC functions for interoperability.
However if the conversion is an offline process meaning you need just to export from mysql and then import into the oracle, that's a different story and you have two options:
1-use the GDAL/OGR tool [here] to do the conversion using the following command: [Recommended]
ogr2ogr -f OCI OCI:user/pass@orcl MySQL:db_name,user=root,password=pass -sql "select * from tabname where fid < 6" -nln target_tname -overwrite -update
lest you forget to download and install the oracle oci driver for gdal.
2-use OGC function in mysql and export the results as a file and then import the file into oracle spatial using again the ogc functions, For example:
mysql> select aswkt(shape_column) from Table_name_With_Geometry ;