"strongly objected" is correct and usable in written English.
You can use it to express strong disapproval or an unwillingness to comply. For example, "My boss strongly objected when I asked for a raise."
Putin strongly objected to U.S. Pres.
Cohl strongly objected to this comparison.
Iran's foreign minister, Mohammad Javad Zarif, strongly objected.
We both strongly objected, and the plan was rejected.
They strongly objected to the process, which they think should be more collaborative.
Privacy advocates strongly objected, saying they did not want more promotional mail from Qwest affiliates.
We believe in privacy, and strongly objected to the N.S.A. turning the little green light on.
"Before he got into it, I strongly objected," Tae Kun Seo says.
Maria strongly objected, on the ground that "Tennessee would never have liked it".
The American Cancer Society also strongly objected to the new recommendations.
The Chinese strongly objected to Washington's latest arms deal with Taiwan.
