In terms of getting the data into the SQL Server database, you can use that ODBC connection directly via the "linked servers" feature (see http://msdn.microsoft.com/en-us/library/ms188279.aspx) - this would allow you to transfer data directly from the remove Oracle instance down to your local SQL Server one with statements as simple as
INSERT <localtable> SELECT <stuff> FROM <server>.<database>.<schema>.<table> WHERE <condition>. I've used this to pull data from both local and remote databases (over VPNs or other tunnels) and found it to be reliable as long as the connectivity between the sites is reliable. It is worth making sure that either your VPN or ODBC setup are performing stream compression: this will increase latency a little but could greatly improve transfer times as your data is most likely to be quite compressible.
Pulling down changes only is going to be something that will depend heavily on the database design.
The best case scenario is if everything is audited so you can easily know which updates have happened since you last picked up changes: check current "last audited action", pull down rows that have been added/changed between that and the last recorded action last time, merge these rows into your local tables, then record the ID/timestamp of the last audited action for next time. The reason to check the audit id/stamp only once at the beginning rather than for each table is to help consistency: you don't have more uptodate data in the tables you transfer last than you do in those you check first. Any other audit/history recording format can be used of course (records holding a "last modified date" and so forth).
If the data has no obvious audit structure like this then things are going to be more convoluted - comparing data in large tables between the two sites is not going to be very efficient. You can reduce the amount of data being transferred by pulling down from each table the primary key column(s) and a hash of all the others, compare the hashes with those generated locally, then request the rows that don't watch locally. You are still going to be transferring something for every row here though (for an UUID PK and a SHA1 hash that is 36 bytes/row plus any padding if transferred in binary form, and it is unlikely to be easily compressible so the VPN can speed it up that way) and if the table contains thinner rows on average than the length of the hash you should transfer the lot as you'll end up doubling (or worse) the transfer with the initial hashes.
You might find you have to use a mix of techniques (updates from audit, checksums for wide tables with no audit, just plain complete transfer for thin tables with no audit) if some of your data is audited and some not.
Another option you might be able to consider (though it requires cooperation from the other end to implement, and may have cost implications as you'll need a local Oracle license) is to use Oracle's equivalent of SQL Server's log shipping method to keep a copy up-to-date on an Oracle instance locally (and move the data from there to SQL Server or Access if that is an explicit requirement rather than just a convenience because that is what you already have installed locally). It is unlikely it that this is possible as an extra for you as it may interfere with the database's primary backup strategy, but if a log shipping equivalent (or differential backups) is being used already for the DB's backup plan then perhaps you could "piggy back" onto the arrangement by having the logs or differential backups sent to you as well as the backup infrastructure. This way the DBMS handles only pushing changes to you (though may push more than by other methods if the same rows are updated many times in the time covered by a given log segment, as you'll get the log of each change to replay not just the final result).
What you are essentially doing with any of the above is emulating replication, so if you have any say on infrastructure or replication is already in use then using that may be an option too.