I don't think the Angels are opposed to having Shohei Ohtani hit and pitch in the same game if his turn in the rotation happens when they're scheduled to play at a National League ballpark. It's something Ohtani did a handful of times in Japan, so it wouldn't be completely new to him.
If Ohtani hadn't sprained his left ankle and had his start pushed back to Sunday, we probably would have seen him hit and pitch in the same game against the Rockies at Coors Field this week. The possibility could present itself again, as the Angels still have Interleague series scheduled at Los Angeles, Arizona and San Diego this season.
For now, Ohtani will be limited to pinch-hitting duties during the Angels' two-game set at Colorado with the designated hitter unavailable.
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Kole Calhoun hasn't started the Angels' past three games against left-handers, so he could see less playing time against lefties if his struggles continue. I think the Angels will still play him regularly against righties to give him a chance to work his way out of his offensive downturn, though.

Someone to keep an eye on at Triple-A Salt Lake is Felix Pena, who has pitched exclusively in relief in the Majors but now appears to be in the process of stretching out as a starter. Pena's last four outings for Salt Lake have been starts, and he's allowed five runs over 12 innings (3.75 ERA) with six walks and 17 strikeouts over that span.
Pena has not thrown more than 76 pitches in an outing, so he still needs to build up his pitch count, but the 28-year-old right-hander is on the Angels' 40-man roster, so he could be an intriguing rotation option if a need arises at some point.
Left-hander John Lamb is also on the depth chart, as he's logged a 3.25 ERA over 27 2/3 innings in seven starts for Salt Lake. Lamb isn't on the 40-man roster, though, so that could be a potential impediment for him. Jesus Castillo and Griffin Canning have been pitching well, but they're still at Double-A Mobile, so they're not as close to impacting the big league club.

I think Jefry Marte is more likely to cut into the playing time of Luis Valbuena than of Jose Pujols, if Marte continues to play well and the rest of the team stays healthy.

Valbuena had been projected to draw most of the starts at first base on days when Pujols served as the DH, but the Angels could be inclined to give Marte more of those opportunities, given his productive start to the season. Pujols is earning $27 million this year and is entrenched as the Angels' cleanup hitter, so if he's healthy, he's going to be in the lineup.
How is Alex Meyer coming along? And will we see him in an Angels uniform this year?
-- Ryan P., Greensburg, Ind.
Meyer resumed throwing last month, so that was a notable milestone in his rehab from right shoulder surgery. When Meyer underwent surgery in September to repair the torn labrum in his shoulder, the Angels estimated that he would miss 12 months, so it's unlikely he will pitch in 2018.