I have a 4x4 stair landing that I want to glue down 3/4" hardwood strips. Since I can't find a small amount of hardwood glue to buy I bought a small pail of parquet glue. Can I use this glue to lay down the hardwood? Will it be strong enough?

Thanks.

Be careful with acrylic, or latex water base glue. Usually parquet is 5/16 inch thick.
It will absorb and then give off extra moisture better than thicker material. It usually has more quarter sawn material, also. A solvent based glue or mastic can work. If you can obtain quarter sawn flooring and follow the directions, you should be OK. You will probably need to get a deep notched trowel, but the directions will tell you what sized gaps for the trowel.

I'm not laying down parquet. Laying down hardwood but using parquet glue. Will this be ok?

Sure you can lay your hardwood with parquet glue. It may not work like you would like it to work, though. It is probably made for 5/16th inch thick parquet.
Read the directions to see if you can glue solid ¾ solid with the glue. If so, it will give you a size for the trowel .The best method would be to use 8d casing nails.
Pre-drill the flooring for the nails every 6 inches at a 45 degree angle with an eighth inch drill.

Thanks for the help.