When it rains water is leaking down the walls of my hhr on the inside of the trim and the car is smelling like mildew. the seatbelts get wet inside of the trim.

lots of ways, to leak rain (or other things)
windshield glass cracked
door seals bad or door warped
heater core, leaking engine coolant, (not water AF50% coolant)
the water in hand feels slimy, is not rain.!!
the cars most have cowl vent area in front of windshield glass.
this cowl when opened UP we see drains if the 2 or more drains Are clogged up with leaves or nests. the cowl floods like a bath tub
and overflows the HVAC fresh air vent, port, (a coffer dam it is)
and flows to the hVAC blower and to the floor., bidda bodda boom.
or super bad rusted car bodies sure do leak.
never ask the blind we can not see your car, blind
find shop tech to find it , living hands on work.

Check the cabin air intake. Chances are the weather strip that lines part of the opening has come off. The intake should be accessible beneath the trim at the base of the windshield on the passenger side.

Had similar on 02 Highlander. Source was leak from around window trim (rust) and roof racks connector entering and going down the windshield post behind the trim. Gently remove interior plastic trim piece to the left of the windshield to investigate any water coming down behind there. Find source, disassemble whatever is required and use something like SupraExpert to seal (not just cheap silicone).

Check all weep holes for clogs below the windshield, it sounds like it may be coming from the fresh air intake. During the heavy rain, it will fill up with water if the weep holes are clogged.

Crawl down there and watch with flashlight while someone sprays area from outside with hose.. when you see where the water is comning in fix it.. this is how a shop would determine where the leak is.. at about $100 an hour.. spray the water gentlly so you can see when it starts comning in. I would suspect windshield seal leak.

GM had a major problem with this issue as models with sunroofs had drain holes that were mfr'd too small. On models without sunroofs, the drains behind the pillars were too small creating the wet/mildewy/dampness issue. All mods were at the expense of the consumer. However if you know a good body and fender man, they can perform this mod for a fairly decent price with excellent results.

Have you been adding any coolant? You could have a leaking heater core, which will usually leak to the inside, wetting the carpets in the well. Most American cars locate the heater core on the passenger side of the firewall, so a leak will typically show up on only the passenger side floor. I once had an Audi that had the heater core mounted just about dead center on the firewall. When it started leaking, both sides of the well(s) got wet.

There is a great possibilty that there is a leak on the Left Side of the Windshield. It is most likely in the area of the upper left side.
The reason for this conclusion is:
The rain water is coming in the Left Upper Side; and either coming down the "A" Pillar, or traveling underneath the trim on the inside roof and coming down the "B" Pillar.
The only other explanantion is a torn, worn, cracked or dislocated Weather Seal on one or both of the doors, allowing rain water to come in. Inspect very carefully these Weather Seals, especially on the top front portion of the rear door.
To help you locate these after a hard rain:
Take the trim panels off the "A: and "B" Pillars and the Roof Line above both Doors. Check for wetness underneath the trim. Or take these trim panels off, and place folded paper towels under the trim panels; reattach the trim panels and wait until it rains. Afterwhich, take these trim panel off and check the paper towels for wetness.
The Windshield Seal is easily inspected for cracks and tears.
Let me know if this helped, or if you have additional information or questions. Feel free to contact me at FixYa.com!

Look under the passenger side of the dash, behind the carpet. Feel the back side of the carpet for dampness. If so, try this: In the same area, look for a black rubber hose that comes from the heater plastic box, and pokes thru the firewall. See if it is plugged up. This is the drain pipe for the AC box, and the cowl panel if the side drains are plugged up. Try that, and please get back to me.

i would check water in radiator as sounds like the heater box under the dash is leaking and will certainly end up on floor