Jack,
The problem occurs when you try to create a string which includes one or more instances of the string delimiter character (which is usually a double quote character).
Access recognises a delimiter character in a string, if the next character following it is also a delimiter character. Thus the name O'Connor could be entered in Access as:
O''Connor if the delimiter character was single quote, or just as O'Connor if the delimiter is a double quote symbol.
I'm unsure of the exact mechanism that you're using to populate your Access tables, but suggest you determine what the delimiter character is (ie. single or double quote). When you've established this, you may then need to do a pre-pass over the data, doubling up on internal quote delimiter characters.
Its kinda hard exactly understanding your question, so I hope that this helps anyway,
Cheers,
Steve