Oppresive as in dark and eerie?

Put a low tone in it.

Rattles - a shaking AC vent is awesome in these instances.

A tree branch tapping a window.

A far-off hissing noise.

Every now and again, a children laughing verbed out like it's coming down from around the corner of a hall you cannot see.

A nice deep rumbly bus going by outside (depending on where it is obviously)

A dog barking outside.

It all depends on the mood you want to create with the audience, and what Oppressive means in this sense. Hope the above helps.

EDIT: Awkwardly Funny Ambience:

Get some funny sounding ambiences like a higher frequency rattle or a funny clock tick.

Also, get the scriptwriter to write something in like a coffee maker drip or a leaky sink where everything else is silent and the two people are staring at each other and the leaky sink keeps falling and then it gets louder and louder and it's awkwardly funny.

Or, write in that the main character taps his fingers over and over on the desk while he's staring at the person.

But again, this is all in pre-prod and I'm sorry if you've been given something to add an awkwardly funny ambience to after it's been shot and edited - which should really be thought with while shooting so instead of having to put obviously recognizable sounds in that are "off screen" because they didn't shoot a close-up of the leaky sink or the tapping of fingers or other things in the environment, you have more leeway to work with things. It's always easier to make a sound work for something you see visually than to make the audience know what they're hearing when it's "off screen" (read: lack of pre-prod).

Well, I'm not sure I understand what you mean about room tone. If you just mean the "airy" feeling that you get from a static room tone, you can try and layer different flavours of room tones, for instance a dark hum layered with a large stone room and put in a bit of airconditioning. You can make it evolve and shift from cut to cut or from location to location.

You can also think about what the environment would sound like, and blend in a bit of traffic, people on the street, sirens, wind, birds, whatever suits the story. If the sounds are too clean, try to muffle them with a reverb that sounds like the room you are trying to describe. You can also EQ it as well, but try the reverb first, print it using Audiosuite, make it 100% wet. If it isn't enough, give it some more reverb on top, like the delay between buildings or a convolution reverb of a pipe or vacuum cleaner hose.

How about some sounds like phones constantly ringing but subtly in the BG? I always find it annoying when they go unanswered for ages in an office environment! Might add a bit if tension/unease to the scene if appropriate? Oh and the constant sounds of photocopiers/printers brings home to me the oppressive, soul sapping nature of tedious offce work! lol

In your case it sounds like "oppressive" needs to be read as "tight" or "confining", rather than low and scary, given the subject matter. If that's correct, then you need to focus on close, claustrophobic sounds, things that will make you shift in your seat and make you want to get some air. My first thought is fluorescent lighting. Nothing says office atmosphere like that. After that I'd try AC vents, computer fans and hard drives, or perhaps a soda machine compressor humming away.

Sounds like a real challenge...good luck!!

Filter some pink noise into reverb. Play just the wet signal and maybe send some of your dialogue track into the verb to make it sound a little more authentic.

one word: fans

Try introducing a tinnitus whine anywhere between 2-4 kHz, it doesn't need to be loud, it will quickly become very annoying and oppressive.

add hum.........

Use and infrasound. Most of the time, they are related to natural disasters: volcanoes, ligthning, earthquakes, avalanches ... Since its not consiously perceived, most people are annoyed, having a weird feeling of fear, like supernatural events are taking place. Sometimes even makes them sick !

Lots of solid ideas here! The only thing I'd add is that I often try to make tones that are either minor chords or specifically are atonal, or at uncomfortable intervals. Depends on if there's a music bed or not, but I like subtly pitching sounds not just higher or lower, but at specific intervals to one another.