Hello
I am assuming that you are moving your site to a shared hosting account. Also depending on your version of OsCommerce, it might need to be upgraded to the latest version because most hosts require sites to operate on PHP 5.x. If your site is very old, it might require PHP 4.x.
So please let me know if any custom work was done to OsCommerce because such custom work, add-ons or upgrades can complicate the upgrade process. Now if you have a dedicated or VPS server at the new host, PHP can be downgraded so either way, it is definitely possible to move the site, but we need to figure out how we'd proceed with the move.
I have been working on OsCommerce sites for 10 years so if you hire me, I can assure you that I would do a good job. I also have more than 10 years of experience with HTML, Javascript, PHP, MySQL, Linux and web development in general.
Thanks,
Danny