How to fix a strong signal strength, yet high packet loss situation?

What you say your IT guy said sounds partially correct. All WIFI devices on the same channel share the same frequency and usage by one user can affect another. Ironically because they are set up with different credentials and parameters the bandwidth can't be used ideally - and of-course, data corruption can occur.

Now note I said "on the same channel". I'll talk about 2.4 gig here, the same principles apply to other frequencies. There are about (depending on your jurisdiction) 11 WIFI channels. Unfortunately they overlap which means there are only 3 - 4 "non-overlapping channels". If different access points use different non-overlapping channels they won't have an issue. Also, even if the channels overlap, if they are far enough away you will still get OK throughput. [ Some AP's automatically look for the best channel ].

There are some things you can do -

1. Co-ordinate with other parties so as to make optimum use of the frequency.
2. Use different gear - the 5 gig band has more capacity and (normally) fewer users. It also has a shorter range.
3. Look at 802.11n equipment with "MIMO" technology, or newer standards with newer versions of corridors/MIMO. This will help "pick out" your signal from the noise.
4. Re-orientate your devices and try different frequencies.
5. Drop support for older standards (802.11b and g) if you can. Each of these standards lowers the amount of frequency available for everyone.
6. Move !!!! (Into a Farraday cage to cut their signals out, or to another building).
7. See if your IT and their IT can "play nice" and create 1 large shared network - that way everyone gets more useable bandwidth - but there are security and cost issues to contend with.

Looking at the part of your question "delay vs packet loss" - they are actually the same thing. Simplisticaly speaking ping tests are done using ICMP or UDP, which is "fire and forget". If a packet is lost or corrupted its thrown out. Websites and email etc generally use TCP which has a mechanism for resending lost packets, thus causing delay rather then packet loss - ie lost packets are retried.

Compounding it - if you look at a "lower level", you will probably find that packets are getting corrupted in-flight, ie 1's are interpreted as 0's or vice-versa - the radio is then throwing them away. While there is limited ability to retransmit, the time frame for doing so is short, and won't help you on a noisy connection. Similarly, if the devices are not all talking the same language (I believe 802.11n does some of this, could be wrong. Newer protocols almost certainly do) they can't reschedule their transmissions to fit together.