These are jar files of SQLite JDBC for OpenVMS, only. They are based on the SQLite JDBC developed by Taro L. Saito, version 3.7.15-M1 (github.com/xerial/sqlite-jdbc ). This is the last version with Java 5.0 support, which in turn is the current Java version for OpenVMS/Alpha. The JDBC driver however works with Java 5.0 and 6.0 available for OpenVMS/Alpha and OpenVMS/I64. The JNIs in the jar files are for SQLITE3 version 3.7.17 (github.com/endlesssoftware) and 3.14.1 (vms-ports - Open Source and Freeware for OpenVMS). The JNI API for Java 8.0 on OpenVMS/I64 changed and therefore its JNI for SQLITE3 version 3.14.1 is in a separate jar file.

The corresponding jar files are sqlite-jdbc-3.7.17-vms.jar, sqlite-jdbc-3.14.1-vms.jar and sqlite-jdbc-3.14.1-vms-j8.jar.

To use the JDBC drivers, just add the jar file to your classpath.

For an initial test, you can try the Sample.java from the SQLite JDBC site, compile it and run it: 

$ java -cp ".:sqlite-jdbc-3.14.1-vms-j8.jar" Sample
name = leo
id = 1
name = yui
id = 2
$

(This program will create a sample.db, which you can access with sqlite3 and its shell.)

This is more or less a proof of concept. It works in my environment, where some more DECC$ and JAVA$ feature logicals were set (configured by JAVA$CONFIG_WIZARD.COM): 
$ define JAVA$CACHING_DIRECTORY TRUE
$ define JAVA$CACHING_INTERVAL 60
$ define JAVA$DAEMONIZE_MAIN_THREAD TRUE
$ define JAVA$DISABLE_CMDFILE_WHITESPACE_PARSING TRUE
$ define JAVA$FILENAME_CONTROLS 8
$ define JAVA$READDIR_CASE_DISABLE TRUE
$ define DECC$EFS_CASE_PRESERVE ENABLE
$ define DECC$FD_LOCKING TRUE
$ define DECC$ARGV_PARSE_STYLE TRUE
$ define DECC$EFS_CASE_PRESERVE TRUE
$ define DECC$EFS_CASE_SPECIAL FALSE
$ define DECC$EFS_CHARSET TRUE
$ define DECC$ENABLE_GETENV_CACHE TRUE
$ define DECC$FILE_PERMISSION_UNIX TRUE
$ define DECC$FILE_SHARING TRUE

For 3.14.1, if you want to use the vms_vfs, the os/vms extension, you need the corresponding shareable images and define these logicals, adjusted to your environment: 
$ define SQLITE3SHR DISK$USER:[Sqlite3.BUILD]sqlite3shr
$ define SQLITE3_OS_EXTENSION sqlite3_vms_vfs
$ define SQLITE3_VMS_VFS DISK$USER:[Sqlite3.BUILD]sqlite3_vms_vfs
But to be honest, I have no idea whether this really works, as the JNI is linked with the SQLite3 objects and sqlite3_vms_vfs is linked against the sqlite3shr and therefore the JNI and the shareable have nothing in common - IF they really need to have.

Anyway, consider defining 
$ define SQLITE3_VMS_OPTIONS "trace:-1"
otherwise you get output like 
OpenVMS VFS module initializing...
--RMS native implementation 1.3.2, override: getcwd,xFullPathname