I have exactly the same problem, with the same noise. It's the strut assembly on the passenger side. Looking around this forum, I notice that those of us with 95/96 model years tend to have this problem. I even wonder if Volvo did a recall on this, it's so common.

A mechanic told me he could do the job for 700 dollars..this is WAY too steep. FPC Groton has several strut assemblies for sale online in the 140 dollar range..170 for the fancy sport ones. The part isn't that expensive, but the job is labor intensive, and it's not a DIY unless you have a spring compressor handy..you could literally decapitate yourself.

I am going to order a new assembly myself next payday and then find a mechanic who can give me a better price, seeing as I will already have the part. It's always better to get the parts yourself because mechanics will be attracted to more expensive ones when shopping for the part so they can increase their markup. If you go armed with the part beforehand, you can cut the cost significantly. I hope to get the job down into the 400 range. Luckily the strut mount assembly can be done by someone not specifically experienced with Volvos, because it's a pretty universal job across the automotive industry.