Oracle most certainly can store them (it can store practically anything you can throw in).
How you store them, well, depends on your app logic/goal:
At one end, you can store a single line per record (e.g. a closed polyline).
At the other end, theoretically, you can store all of them in one record, in one field (one single multiline) - not practical at all.
You can also store one multiline per altitude value (one row, one multiline, for 10m, another one for 20m etc).
Oracle also supports multiple geometry columns in the same table (even of different types of geometry), but it wouldn't be easy to find an application that could display that (in most, you would have to create one 'layer' per geometry column of the table).
In between those options, you must find the implementation that works best for your business logic - the combinations can cover pretty much any case.
At the end, it all depends on the total number of nodes (resolution+dataset), on how you plan to use this table (what kind of queries/processes you'll run) and on your hardware (CPU, RAM, Oracle version).
It is a very common requirement and an optimal implementation can easily be made (I work with millions of geometries in Oracle, every day, with hardly any GUI at all).
Without any info about your dataset I can hardly be anything more than theoretical, but, closing, one of the most common and versatile scenarios would be to store each contour as a single record, with the altitude value as an attribute (e.g. ID, ALT_VALUE, GEOMETRY).