Or perhaps even 日本語実力程度? Although that seems overkill and double emphasising.
1 Answer
It depends on the context, but both 日本語程度 and 日本語実力 strike me as very noun dense. It's much more natural to insert particles and make them a noun phrase, like 日本語の程度 and 日本語の実力, unless it's used in a context that demands the noun dense form, like 日本語実力検定試験 or as a newspaper title.
程度 can refer to the level neutrally, but it often carries the loaded meaning of low level/rank and lack of mastery, such as 百姓程度で生意気な "how dare a farmer say that!" So when I hear 日本語程度 I mentally picture a sentence to follow that says something about Japanese not so blah blah, for example 日本語程度では苦労しないよ.