OSB is one of many engineered wood products used in home construction. Many of these products are less expensive as they are easier to produce, and thus are popular among builders looking to slice pennies off of projects. First, let me respond to your structural concerns about OSB and then we'll tackle the health issues.
For the most part, I have no concerns about the use of OSB in home construction. When properly nailed as a sidewall sheathing (eight nails at the seam, six nails in the field), OSB is just as functional as plywood at preventing racking, a sideways movement of the framed wall. OSB works just as well for floor sheathing, so long as the OSB is thick enough and in tongue-and-groove form so that all boards lock together.
The one area of home construction where I really don't like to see OSB used is as roof sheathing. In my 20-plus years of experience as a professional home inspector, I frequently noticed that OSB roofs were very wavy. Since OSB is not as stiff as plywood, it would flex around every roof rafter or truss. If one of these ended up being high or sagged, you'd see an obvious hump or sag in the roof right over that spot. I also felt very uncomfortable walking on an OSB-sheathed roof as it was much weaker than, say, the cheapest half-inch plywood. Finally, I also noticed that roofing shingle nails don't seem to have the same holding power with OSB as they do with plywood. As a result, you see a lot more roof shingles blown off of an OSB roof than a plywood one.
As for health effects, there have always been concerns about off-gassing of the glues in OSB. But the research shows that this off-gassing is so minimal that it should not have an impact on health--that is, unless your parents happen to be very chemically sensitive, in which case all bets are off.
More detail on the topic is published by TECO, a US-based third-party certification and testing agency of structural panel products. TECO evaluates and certifies OSB, plywood, particleboard, MDF and agrifiber panels produced throughout North, Central and South America, as well as Europe.
According to TECO's experts, structural panels such as OSB and plywood that are manufactured with exterior-type phenol formaldehyde and isocyanate adhesives do not off-gas like other types of wood-based panels, and therefore do not require certification for formaldehyde emissions. Phenolic-based adhesives are specifically exempted in Section II.C.3 of HUD Rule 24 CFR 3280 (of the August 9, 1984 Federal Register), which states that HUD "has decided to exempt products that are formulated exclusively with phenol-formaldehyde resins and surface finishes from the testing and certification provision of the rule." The amount of formaldehyde emitted from panels using phenolic-based adhesives is considered too small to be significant and has therefore been exempted. Isocyanate resin panels do not contain formaldehyde so no risk of formaldehyde emissions exists.
For more information on OSB safety in home construction and an in-depth explanation of rules around formaldehyde emissions in wood-based panels, please refer to TECO's Tech Tip, "Formaldehyde Emissions from Wood-Based Panels."